text
stringlengths 73
2.82k
| category
stringclasses 21
values |
|---|---|
Higher-order Time-Delay Interferometry: Time-Delay Interferometry (TDI) is the data processing technique that cancels
the large laser phase fluctuations affecting the one-way Doppler measurements
made by unequal-arm space-based gravitational wave interferometers. In a
previous publication we derived TDI combinations that exactly cancel the laser
phase fluctuations up to first order in the inter-spacecraft velocities. This
was done by interfering two digitally-synthesized optical beams propagating a
number of times clock- and counter-clock-wise around the array. Here we extend
that approach by showing that the number of loops made by each beam before
interfering corresponds to a specific higher-order TDI space. In it the
cancellation of laser noise terms that depend on the acceleration and
higher-order time derivatives of the inter-spacecraft light-travel-times is
achieved exactly. Similarly to what we proved for the second-generation TDI
space, elements of a specific higher-order TDI space can be obtained by first
``lifting'' the basis ($\a, \b, \g, X$) of the $1^{\rm st}$-generation TDI
space to the higher-order space of interest and then taking linear combinations
of them with coefficients that are polynomials of the six delays operators.
Higher-Order TDI might be required by future interplanetary gravitational wave
missions whose inter-spacecraft distances vary appreciably with time, in
particular, relative velocities are much larger than those of currently planned
arrays. | gr-qc |
Mode decomposition and unitarity in quantum cosmology, Talk given at the
Second Meeting on Constrained Dynamics and Quantum gravity, Santa Margherita
Ligure, September 17-21, 1996: Contrary to common belief, there are perspectives for generalizing the notion
of positive and negative frequency in minisuperspace quantum cosmology, even
when the wave equation does not admit symmetries. We outline a strategy in
doing so when the potential is positive. Also, an underlying unitarity
structure shows up. Starting in the framework of the Klein-Gordon type
quantization, I am led to a result that relies on global features on the model,
and that is possibly related to structures encountered in the refined algebraic
quantization scheme. | gr-qc |
Self-force on a static particle near a black hole: We study the self-force acting on a static charged point-like particle near a
Schwarzschild black hole. We obtain the point-like particle as a limit of a
spacetime describing a big neutral black hole with a small charged massive
object nearby. The massive object is modeled by a black hole or a naked
singularity. In this fully interacting system the massive object is supported
above the black hole by a strut. Such a strut has a non-zero tension which
corresponds to the external force compensating the gravitational force and the
electromagnetic self-force acting on the massive object. We discuss details of
the limiting procedure leading to the point-like particle situation. As a
result, we obtain the standard gravitational force in the static frame of the
Schwarzschild spacetime and the electromagnetic self-force. The
electromagnetic-self force differs slightly from the classical results in a
domain near the horizon. The difference is due to taking into account an
influence of the strut on the electromagnetic field. We also demonstrate that
higher order corrections to the gravitational force, a sort of the
gravitational self-force, are not uniquely defined and they depend on details
of the limiting procedure. | gr-qc |
Variables suitable for constructing quantum states for the Teleparallel
Equivalent of General Relativity II: We present the second (and final) part of an analysis aimed at introducing
variables which are suitable for constructing a space of quantum states for the
Teleparallel Equivalent of General Relativity. In the first part of the
analysis we introduced a family of variables on the "position" sector of the
phase space. In this paper we distinguish differentiable variables in the
family. Then we define momenta conjugate to the distinguished variables and
express constraints of the theory in terms of the variables and the momenta.
Finally, we exclude variables which generate an obstacle for further steps of
the Dirac's procedure of canonical quantization of constrained systems we are
going to apply to the theory. As a result we obtain two collections of
variables on the phase space which will be used (in a subsequent paper) to
construct the desired space of quantum states. | gr-qc |
Classical and quantum cosmology of Fab Four John theories: We present here a quantum cosmological model with Bohm-de Broglie
interpretation of the theory described by a combination of two terms of the Fab
Four cosmological theory. The first term is the John Lagrangian and the second
is a potential representing matter content to avoid classical trivial
solutions. This model has two free functions that provide an adjustment
mechanism known classically as self-tuning. The self-tuning is a way to address
the cosmological constant problem by allowing a partial break of symmetry in
the scalar field sector. The Fab Four is the most general set of self-tuning
scalar-tensor gravitational theories in four dimensions. The minisuperspace
Hamiltonian thus obtained from this combination of Fab Four terms has
fractional powers in the momenta, leading to a problem in applying canonical
quantization. We have solved this problem by generalizing the canonical
quantization rule using the so-called conformable fractional derivative. We
show that this analysis leads to both singular and bouncing (non-singular)
solutions, depending on the initial conditions over the scale factor and the
homogeneous scalar field, and also depending on the free functions mentioned.
This provides an adjustment mechanism in analogy with the classical self-tuning
of the Fab Four, but with another interpretation. | gr-qc |
The generalized $sl(2, R)$ and $su(1, 1)$ in non-minimal constant-roll
inflation: In the present work, we consider the non-minimal coupling inflationary model
in the context of the constant-roll idea which is investigated by the
first-order formalism. We attempt to find the hidden symmetries behind the
model by the Lie symmetry method. We supply this aim by using the symmetry
features of the Heun function instead of Killing vector approach. We show that
the hidden symmetries of the non-minimal constant-roll inflation in the cases
of power-law and exponential couplings are characterized as a generalized form
of $sl(2, R)$ and $su(1, 1)$ algebra, respectively. | gr-qc |
Orbital effects of Lorentz-violating Standard Model Extension
gravitomagnetism around a static body: a sensitivity analysis: We analytically work out the long-term rates of change of the six osculating
Keplerian orbital elements of a test particle acted upon by the
Lorentz-violating gravitomagnetic acceleration due to a static body, as
predicted by the Standard Model Extension (SME). We neither restrict to any
specific spatial orientation for the symmetry-violating vector s nor make a
priori simplifying assumptions concerning the orbital configuration of the
perturbed test particle. Thus, our results are quite general, and can be
applied for sensitivity analyses to a variety of specific astronomical and
astrophysical scenarios. We find that, apart from the semimajor axis a, all the
other orbital elements undergo non-vanishing secular variations. By comparing
our results to the latest determinations of the supplementary advances of the
perihelia of some planets of the solar system we preliminarily obtain s_x =
(0.9 +/- 1.5) 10^-8, s_y = (-4 +/- 6) 10^-9, s_z = (0.3 +/- 1) 10^-9. Bounds
from the terrestrial LAGEOS and LAGEOS II satellites are of the order of s\sim
10^-3-10^-4. | gr-qc |
On the Nature of the Cosmological Constant Problem: General relativity postulates the Minkowski space-time to be the standard
flat geometry against which we compare all curved space-times and the
gravitational ground state where particles, quantum fields and their vacuum
states are primarily conceived. On the other hand, experimental evidences show
that there exists a non-zero cosmological constant, which implies in a deSitter
space-time, not compatible with the assumed Minkowski structure. Such
inconsistency is shown to be a consequence of the lack of a application
independent curvature standard in Riemann's geometry, leading eventually to the
cosmological constant problem in general relativity.
We show how the curvature standard in Riemann's geometry can be fixed by
Nash's theorem on locally embedded Riemannian geometries, which imply in the
existence of extra dimensions. The resulting gravitational theory is more
general than general relativity, similar to brane-world gravity, but where the
propagation of the gravitational field along the extra dimensions is a
mathematical necessity, rather than being a a postulate. After a brief
introduction to Nash's theorem, we show that the vacuum energy density must
remain confined to four-dimensional space-times, but the cosmological constant
resulting from the contracted Bianchi identity is a gravitational contribution
which propagates in the extra dimensions. Therefore, the comparison between the
vacuum energy and the cosmological constant in general relativity ceases to be.
Instead, the geometrical fix provided by Nash's theorem suggests that the
vacuum energy density contributes to the perturbations of the gravitational
field. | gr-qc |
The sound of DHOST: We show that, in generic higher-order scalar-tensor theories which avoid the
Ostrogradsky instability, the presence of a scalar field significantly modifies
the propagation of matter perturbations, even in weakly curved backgrounds.
This affects notably the speed of sound in the atmosphere of the Earth. It can
also generate instabilities in homogeneous media. We use this to constrain the
viable higher-order scalar-tensor models. | gr-qc |
Constraining the parameters of GW150914 & GW170104 with numerical
relativity surrogates: Gravitational-wave detectors have begun to observe coalescences of heavy
black holes at a consistent pace for the past few years. Accurate models of
gravitational waveforms are essential for unbiased and precise estimation of
source parameters. Recently developed surrogate models based on high-accuracy
numerical relativity (NR) simulations are ideal for constraining physical
parameters of heavy black hole merger events. In this paper, we first
demonstrate the viability of these multi-modal surrogates as reliable parameter
estimation tools. We show that NR surrogates can extract additional information
from GW data that is inaccessible to traditional models, by analyzing a set of
synthetic signals with the NR surrogate and other approximants.
We also consider the case of two of the earliest binary black holes detected
by the LIGO observatories: GW150914 and GW170104. We reanalyze their data with
fully-precessing NR-surrogate templates and freely provide the resulting
posterior samples as supplemental material. We find that our refined analysis
is able to extract information from sub-dominant GW harmonics in data, and
therefore better resolve the degeneracy in measuring source luminosity distance
and orbital inclination for both events. We estimate the sources of both events
to be 20-25% further away than was previously estimated. Our analyses also
constrain their orbital orientation more tightly around face-on or face-off
configurations than before. Additionally, for GW150914 we constrain the
effective inspiral spin more tightly around zero. This work is one of the first
to unambiguously extract sub-dominant GW mode information from real events. It
is also a first step toward eliminating the approximations used in
semi-analytic waveform models from GW parameter estimation. It also motivates
that NR surrogates be extended to cover more of the binary black hole parameter
space. | gr-qc |
Black hole solution in third order Lovelock gravity has no Gauss-Bonnet
limit: We revisit the spherically symmetric third order Lovelock black hole solution
in 7-dimensions. We show that the general solution for the metric function does
not admit the Gauss-Bonnet (GB) limit. This is not expected due to the linear
superposition of the second (GB) and third order Lovelock Lagrangians in the
general action. It is found that the two branches of the GB solutions are
indeed the limit of the other two complex solutions of the field equations in
the third order Lovelock gravity. These two complex solutions could not be
accepted as the solutions of the Einstein's field equations which are supposed
to be real values function on entire real r- axis. A new solution which is only
valid if the third order Lovelock parameter is small is introduced which can be
considered as the natural extension of the general relativity (GR) to the third
order Lovelock modified theory of gravity. We also generalize the discussion to
the higher dimensional third order Lovelock gravity coupled to the matter
sources with cosmological constant. | gr-qc |
Dark matter interacts with variable vacuum energy: We investigate a spatially flat Friedmann-Robertson-Walker (FRW) scenario
with two interacting components, dark matter and variable vacuum energy (VVE)
densities, plus two decoupled components, one is a baryon term while the other
behaves as a radiation component. We consider a linear interaction in the
derivative dark component density. We apply the $\chi^2$ method to the
observational Hubble data for constraining the cosmological parameters and
analyze the amount of dark energy in the radiation era for the model. It turns
out that our model fulfills the severe bound of $\Omega_{x}(z\simeq
1100)<0.009$ at $2\sigma$ level, so is consistent with the recent analysis that
includes cosmic microwave background anisotropy measurements from Planck
survey, the future constraints achievable by Euclid and CMBPol experiments,
reported for the behavior of the dark energy at early times, and fulfills the
stringent bound $\Omega_{x}(z\simeq 10^{10})<0.04$ at $2\sigma$ level in the
big-bang nucleosynthesis epoch. We also examine the cosmic age problem at high
redshift associated with the old quasar APM 08279+5255 and estimate the age of
the universe today. | gr-qc |
Deformed black hole immersed in dark matter spike: If a lot of dark matter particles accumulate near the black hole, then the
chances of detecting dark matter signals near a black hole are greatly
increased. These effects may be observed by the Event Horizon Telescope (EHT),
Tianqin project, Taiji project, Laser Interferometer Space Antenna (LISA) and
Laser Interferometer Gravitational-Wave Observatory (LIGO). In this work, we
explore the effects of dark matter spikes on black hole space-time. For the
Schwarzschild-like black hole case, we consider Newton$'$s approximation and
perturbation approximation. This makes it possible to use Xu$'$s method to
solve the Einstein field equation, and extend Schwarzschild-like black hole to
Kerr-like black hole (BH) via Newman-Janis (NJ) algorithm. By analyzing the
dark matter spike on the black hole event horizon (EH), stationary limit
surfaces (SLS), ergosphere and energy-momentum tensors (EMT), we found that
compared with the dark matter halo, the dark matter spike would have a higher
effect on the black hole by several orders of magnitude. Therefore, if there is
a dark matter spike near the black hole, it is very possible to test the dark
matter model through gravitational wave (GW) observation and EHT observation. | gr-qc |
Analysis of GWTC-3 with fully precessing numerical relativity surrogate
models: The third Gravitational-Wave Transient Catalog (GWTC-3) contains 90 binary
coalescence candidates detected by the LIGO-Virgo-KAGRA Collaboration (LVK). We
provide a re-analysis of binary black hole (BBH) events using a recently
developed numerical relativity (NR) waveform surrogate model, NRSur7dq4, that
includes all $\ell \leq 4$ spin-weighted spherical harmonic modes as well as
the complete physical effects of precession. Properties of the remnant black
holes' (BH's) mass, spin vector, and kick vector are found using an associated
remnant surrogate model NRSur7dq4Remnant. Both NRSur7dq4 and NRSur7dq4Remnant
models have errors comparable to numerical relativity simulations and allow for
high-accuracy parameter estimates. We restrict our analysis to 47 BBH events
that fall within the regime of validity of NRSur7dq4 (mass ratios greater than
1/6 and total masses greater than $60 M_{\odot}$). While for most of these
events our results match the LVK analyses that were obtained using the
semi-analytical models such as IMRPhenomXPHM and SEOBNRv4PHM, we find that for
more than 20\% of events the NRSur7dq4 model recovers noticeably different
measurements of black hole properties like the masses and spins, as well as
extrinsic properties like the binary inclination and distance. For instance,
GW150914_095045 exhibits noticeable differences in spin precession and spin
magnitude measurements. Other notable findings include one event
(GW191109_010717) that constrains the effective spin $\chi_{eff}$ to be
negative at a 99.3\% credible level and two events (GW191109_010717 and
GW200129_065458) with well-constrained kick velocities. Furthermore, compared
to the models used in the LVK analyses, NRSur7dq4 recovers a larger
signal-to-noise ratio and/or Bayes factors for several events. | gr-qc |
The Smallest Shape Spaces. III. Triangles in 2- and 3-d: This is an innovative treatise on triangles, resting upon 1) 3-body problem
techniques including mass-weighted relative Jacobi coordinates. 2) Part I's
detailed layer-by-layer topological and geometrical study of Kendall-type shape
spaces - configuration spaces of all possible shapes - which, for triangles,
are (pieces of) spheres. 3) Hopf mathematics. Triangles are moreover
prototypical through being the smallest models which carry relative-angle as
well as length-ratio information. Both 1) and 3) produce insightful new
versions of Heron's formula, 3)'s simultaneously providing new foundations for
2). Medians, and regular triangles bounding between tall and flat triangles,
also play prominent roles. Right triangles form three kissing cap-circles on
the shape sphere, from which a shape-theoretic answer to the well-known
conundrum of what is the probability that a triangle is obtuse very readily
follows: 3/4. The differential-geometric aspects of this answer moreover
generalize to numerous variant problems.
Hopf mathematics additionally gives a general bundle section interpretation
to Kendall's iconic spherical blackboard of vertex-unlablelled
mirror-image-identified triangles, and of its two variants where one of these
two conditions are dropped. We attribute a monopole to each of these spaces and
to the full shape sphere, one due to Dirac, one to Iwai and the other two are
new to this paper. We finally make insightful comparison of triangles in 2-$d$
with a) Part II's 4 points on the line. b) Triangles in 3-$d$, which are
particularly significant as the smallest model exhibiting stratification.
Stratified manifold-sheaf pairs - sheaves adding useful local and global
structure to general bundles - lie at the heart of Shape Theory's future
development. | gr-qc |
The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well
behaved: We show that the Big Bang singularity of the
Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to
General Relativity. We prove a theorem showing that the Einstein equation can
be written in a non-singular form, which allows the extension of the spacetime
before the Big Bang. The physical interpretation of the fields used is
discussed. These results follow from our research on singular semi-Riemannian
geometry and singular General Relativity. | gr-qc |
On the (non) existence of a gravitomagnetic Dynamo: Due to the resemblance between Maxwell and the gravitomagnetic equations
obtained in the weak field and slow motion limit of General Relativity, one can
ask if it is possible to amplify a seed intrinsic rotation or spin motion by a
gravitomagetic dynamo, in analogy with the well-known dynamo effect. Using the
Galilean limits of the gravitomagnetic equations, the answer to this question
is negative, due to the fact that a "magnetic" Galilean limit for the
gravitomagnetic equations is physically inconsistent. | gr-qc |
Density-metric unimodular gravity: vacuum maximal symmetry: We have investigated the vacuum maximally symmetric solutions of recently
proposed density-metric unimodular gravity theory,the results are widely
different from inflationary senario.The exponential dependence on time in
deSitter space is substiuted by a power law. Open space-times with non-zero
cosmological constant are excluded in this theory | gr-qc |
The Cosmological Constant from Conformal Transformations: Möbius
Invariance and Schwarzian Action: The homogeneous Friedman-Lema\^\i tre-Robertson-Walker (FLRW) cosmology of a
free scalar field with vanishing cosmological constant was recently shown to be
invariant under the one-dimensional conformal group $\textrm{SL}(2,\mathbb{R})$
acting as M{\"o}bius transformations on the proper time. Here we generalize
this analysis to arbitrary transformations of the proper time, $\tau\mapsto
\tilde{\tau}=f(\tau)$, which are not to be confused with reparametrizations of
the time coordinate. First, we show that the FLRW cosmology with a
non-vanishing cosmological constant $\Lambda\ne 0$ is also invariant under a
$\textrm{SL}(2,\mathbb{R})$ group of conformal transformations. The associated
conformal Noether charges form a $\mathfrak{sl}(2,\mathbb{R})$ Lie algebra
which encodes the cosmic evolution. Second, we show that a cosmological
constant can be generated from the $\Lambda=0$ case through particular
conformal transformations, realizing a compactification or de-compactification
of the proper time depending on the sign of $\Lambda$. Finally, we propose an
extended FLRW cosmological action invariant under the full group
$\textrm{Diff}({\cal S}^1)$ of conformal transformations on the proper time, by
promoting the cosmological constant to a gauge field for conformal
transformations or by modifying the scalar field action to a Schwarzian action.
Such a conformally-invariant cosmology leads to a renewed problem of time and
to the necessity to re-think inflation in purely time-deparameterized terms. | gr-qc |
Improved approximate inspirals of test-bodies into Kerr black holes: We present an improved version of the approximate scheme for generating
inspirals of test-bodies into a Kerr black hole recently developed by
Glampedakis, Hughes and Kennefick. Their original "hybrid" scheme was based on
combining exact relativistic expressions for the evolution of the orbital
elements (the semi-latus rectum p and eccentricity e) with approximate,
weak-field, formula for the energy and angular momentum fluxes, amended by the
assumption of constant inclination angle, iota, during the inspiral. Despite
the fact that the resulting inspirals were overall well-behaved, certain
pathologies remained for orbits in the strong field regime and for orbits which
are nearly circular and/or nearly polar. In this paper we eliminate these
problems by incorporating an array of improvements in the approximate fluxes.
Firstly, we add certain corrections which ensure the correct behaviour of the
fluxes in the limit of vanishing eccentricity and/or 90 degrees inclination.
Secondly, we use higher order post-Newtonian formulae, adapted for generic
orbits. Thirdly, we drop the assumption of constant inclination. Instead, we
first evolve the Carter constant by means of an approximate post-Newtonian
expression and subsequently extract the evolution of iota. Finally, we improve
the evolution of circular orbits by using fits to the angular momentum and
inclination evolution determined by Teukolsky based calculations. As an
application of the improved scheme we provide a sample of generic Kerr
inspirals and for the specific case of nearly circular orbits we locate the
critical radius where orbits begin to decircularise under radiation reaction.
These easy-to-generate inspirals should become a useful tool for exploring LISA
data analysis issues and may ultimately play a role in source detection. | gr-qc |
Action and Observer dependence in Euclidean quantum gravity: Given a Lorentzian spacetime $(M, g)$ and a non-vanishing timelike vector
field $u(\lambda)$ with level surfaces $\Sigma$, one can construct on $M$ a
Euclidean metric $g_E^{ab} = g^{ab} + 2 u^a u^b$. Motivated by this, we
consider a class of metrics $\hat{g}^{ab} = g^{ab} - \Theta(\lambda)\, u^a u^b$
with an arbitrary function $\Theta$ that interpolates between the Euclidean
($\Theta=-2$) and Lorentzian ($\Theta=0$) regimes. The Euclidean regime is in
general different from that obtained from Wick rotation $t \rightarrow - i t$.
For example, if $g_{ab}$ is the $k=0$ Lorentzian de Sitter metric corresponding
to $\Lambda>0$, the Euclidean regime of $\hat{g}_{ab}$ is the $k=0$ Euclidean
anti-de Sitter space with $\Lambda<0$. We analyze the curvature tensors
associated with $\hat{g}$ for arbitrary Lorentzian metrics $g$ and timelike
geodesic fields $u^a$, and show that they have interesting and remarkable
mathematical structures: (i) Additional terms arise in the Euclidean regime
$\Theta \to -2$ of $\hat{g}_{ab}$. (ii) For the simplest choice of a step
profile for $\Theta$, the Ricci scalar Ric$[\widehat{g}]$ of $\hat{g}_{ab}$
reduces, in the Lorentzian regime $\Theta \to 0$, to the complete
Einstein-Hilbert lagrangian with the correct Gibbons-Hawking-York boundary
term; the latter arises as a delta-function of strength $2K$ supported on
$\Sigma_0$. (iii) In the Euclidean regime $\Theta \to -2$, Ric$[\hat{g}]$ also
has an extra term $2\, {}^3 R$ of the $u$-foliation. We highlight similar
foliation dependent terms in the full Riemann tensor. We present some explicit
examples and briefly discuss implications of the results for Euclidean quantum
gravity and quantum cosmology. | gr-qc |
Plane symmetric traversable wormholes in an anti-de Sitter background: We construct solutions of plane symmetric wormholes in the presence of a
negative cosmological constant by matching an interior spacetime to the
exterior anti-de Sitter vacuum solution. The spatial topology of this plane
symmetric wormhole can be planar, cylindrical and toroidal. As usual the null
energy condition is necessarily violated at the throat. At the junction
surface, the surface stresses are determined. By expressing the tangential
surface pressure as a function of several parameters, namely, that of the
matching radius, the radial derivative of the redshift function and of the
surface energy density, the sign of the tangential surface pressure is
analyzed. We then study four specific equations of state at the junction: zero
surface energy density, constant redshift function, domain wall equation of
state, and traceless surface stress-energy tensor. The equation governing the
behavior of the radial pressure, in terms of the surface stresses and the
extrinsic curvatures, is also displayed. Finally, we construct a model of a
plane symmetric traversable wormhole which minimizes the usage of the exotic
matter at the throat, i.e., the null energy condition is made arbitrarily small
at the wormhole throat, while the surface stresses on the junction surface
satisfy the weak energy condition, and consequently the null energy condition.
The construction of these wormholes does not alter the topology of the
background spacetime (i.e., spacetime is not multiply-connected), so that these
solutions can instead be considered domain walls. Thus, in general, these
wormhole solutions do not allow time travel. | gr-qc |
Quasinormal modes of renormalization group improved Dymnikova regular
black holes: We find accurate quasinormal frequencies of a quantum corrected black hole
constructed in the renormalization group theory via the coordinate-independent
iterative procedure, leading to the Dymnikova regular black hole. We show that
while the fundamental mode is only slightly affected by the quantum correction,
the overtones change at a much stronger rate. This outburst of overtones occurs
because of the deformation of the geometry of the Schwarzschild black hole
solely near the event horizon. For finding accurate values of overtones we
developed a general procedure allowing one to use the Leaver method to metrics
which, initially, are not expressed in terms of rational functions. | gr-qc |
Geodesic equations in the static and rotating dilaton black holes:
Analytical solutions and applications: In this paper, we consider the timelike and null geodesics around the static
[GMGHS (Gibbons, Maeda, Garfinkle, Horowitz and Strominger), magnetically
charged GMGHS, electrically charged GMGHS] and the rotating (Kerr-Sen
dilaton-axion) dilaton black holes. The geodesic equations are solved in terms
of Weierstrass elliptic functions. To classify the trajectories around the
black holes, we use the analytical solution and effective potential techniques
and then characterize the different types of the resulting orbits in terms of
the conserved energy and angular momentum. Also, using the obtained results we
study astrophysical applications. | gr-qc |
On Nash theory of gravity with matter contents: Although it was proved that the Nash theory doesn't have classical Einstein
limits, it has been proven to be formally divergent free and considered to be
of interest in constructing theories of quantum gravity. The original Nash
gravity without matter contents can't explain the current accelerated expansion
of the Universe. A possible extension of theory is by adding some matter
contents to the model. In this work, we generalize the Nash theory of gravity
by adding the matter fields. In order to examine the effects of this
generalization, we first derive the equations of motion in the flat FLRW
spacetime and examine the behaviors of the solutions by invoking specific forms
of the Hubble parameter. We also classify the physical behaviors of the
solutions by employing the stability analysis and check the consistency of the
model by considering particular cosmological parameters. | gr-qc |
Orthogonal decomposition of Lorentz transformations: The canonical decomposition of a Lorentz algebra element into a sum of
orthogonal simple (decomposable) Lorentz bivectors is discussed, as well as the
decomposition of a proper orthochronous Lorentz transformation into a product
of commuting Lorentz transformations, each of which is the exponential of a
simple bivector. As an application, we obtain an alternative method of deriving
the formulas for the exponential and logarithm for Lorentz transformations. | gr-qc |
On periodic solutions of nonlinear wave equations, including Einstein
equations with a negative cosmological constant: Original abstract: "We construct periodic solutions of nonlinear wave
equations using analytic continuation. The construction applies in particular
to Einstein equations, leading to infinite-dimensional families of
time-periodic solutions of the vacuum, or of the
Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$
equations, with a negative cosmological constant." However, there is a gap in
the proof, and it is unlikely that the strategy presented can be upgraded to a
full proof. | gr-qc |
Constraints on a charge in the Reissner--Nordström metric for the
black hole at the Galactic Center: Using an algebraic condition of vanishing discriminant for multiple roots of
fourth degree polynomials we derive an analytical expression of a shadow size
as a function of a charge in the Reissner -- Nordstr\"om (RN) metric
\cite{Reissner_16,Nordstrom_18}. We consider shadows for negative tidal charges
and charges corresponding to naked singularities $q=\mathcal{Q}^2/M^2 > 1$,
where $\mathcal{Q}$ and $M$ are black hole charge and mass, respectively, with
the derived expression. An introduction of a negative tidal charge $q$ can
describe black hole solutions in theories with extra dimensions, so following
the approach we consider an opportunity to extend RN metric to negative
$\mathcal{Q}^2$, while for the standard RN metric $\mathcal{Q}^2$ is always
non-negative. We found that for $q > 9/8$ black hole shadows disappear.
Significant tidal charges $q=-6.4$ (suggested by Bin-Nun (2010)) are not
consistent with observations of a minimal spot size at the Galactic Center
observed in mm-band, moreover, these observations demonstrate that a Reissner
-- Nordstr\"om black hole with a significant charge $q \approx 1$ provides a
better fit of recent observational data for the black hole at the Galactic
Center in comparison with the Schwarzschild black hole. | gr-qc |
Hamiltonian perturbation theory in f(R) gravity: Hamiltonian perturbation theory is used to analyse the stability of f(R)
models. The Hamiltonian equations for the metric and its momentum conjugate are
written for f(R) Lagrangian in the presence of perfect fluid matter. The
perturbations examined are perpendicular to R. As perturbations are added to
the metric and momentum conjugate to the induced metric instabilities are
found, depending on the form of f(R). Thus the examination of these
instabilities is a way to rule out certain f(R) models. | gr-qc |
Entropy of massive fields near a black hole and vacuum polarization:
thermodynamics without statistical mechanics: Starting from the Frolov-Zel'nikov stress-energy tensor of quantum massive
fields in the Schwarzschild background, we recover the contribution $S_{q}$ of
these field into the entropy of a black hole. For fermions with the spin
$%s=1/2$ $S_{q}>0$, for scalar fields $S_{q}>0$ provided the coupling parameter
is restricted to some interval, and $S_{q}<0$ for vector fields. The appearance
of negative values of $S_{q}$ is attributed to the fact that in the situation
under discussion there are no real quanta to contribute to the entropy, so
$S_{q}$ is due to vacuum polarization entirely and has nothing to do with the
statistical-mechanical entropy. We also consider the spacetime with an
acceleration horizon - the Bertotti-Robison spacetime - and show that $S_{q}=0$
for massive fields similarly to what was proved earlier for massless fields. | gr-qc |
Hubble multi-scalar inflation: Multiple field models of inflation exhibit new features than single field
models. In this work, we study the hierarchy of parameters based on Hubble
expansion rate in curved field space and derive the system of flow equations
that describe their evolution. Then we focus on obtaining derivatives of number
of $e$-folds with respect to scalar fields during inflation and at hypersurface
of the end of inflation. | gr-qc |
An Anisotropic Wormhole:TUNNELLING in Time and Space: We discuss the structure of a gravitational euclidean instanton obtained
through coupling of gravity to electromagnetism. Its topology at fixed $t$ is
$S^1\times S^2$. This euclidean solution can be interpreted as a tunnelling to
a hyperbolic space (baby universe) at $t=0$ or alternatively as a static
wormhole that joins the two asymptotically flat spaces of a
Reissner--Nordstr\"om type solution with $M=0$. | gr-qc |
Non-equilibrium evolution of quantum fields during inflation and late
accelerating expansion: To understand mechanisms leading to inflation and late acceleration of the
Universe it is important to see how one or a set of quantum fields may evolve
such that the classical energy-momentum tensor behave similar to a cosmological
constant. In this work we consider a toy model including 3 scalar fields with
very different masses to study the formation of a light axion-like condensate,
presumed to be responsible for inflation and/or late accelerating expansion of
the Universe. Despite its simplicity, this model reflects hierarchy of masses
and couplings of the Standard Model and its candidate extensions. The
investigation is performed in the framework of non-equilibrium quantum field
theory in a consistently evolved FLRW geometry. We discuss in details how the
initial conditions for such a model must be defined in a fully quantum setup
and show that in a multi-component model interactions reduce the number of
independent initial degrees of freedom. Numerical simulation of this model
shows that it can be fully consistent with present cosmological observations.
For the chosen range of parameters we find that quantum interactions rather
than effective potential of a condensate is the dominant contributor in the
energy density of the Universe and triggers both inflation and late
accelerating expansion. Nonetheless, despite its small contribution in the
energy density, the light scalar field - in both condensate and quasi free
particle forms - has a crucial role in controlling the trend of heavier fields.
Furthermore, up to precision of our simulations we do not find any IR
singularity during inflation. These findings highlight uncertainties in
attempts to extract information about physics of the early Universe by naively
comparing predictions of local effective classical models with cosmological
observations, neglecting inherently non-local nature of quantum processes. | gr-qc |
The effective Tolman temperature in curved spacetimes: We review a recently proposed effective Tolman temperature and present its
applications to various gravitational systems. In the Unruh state for the
evaporating black holes, the free-fall energy density is found to be negative
divergent at the horizon, which is in contrast to the conventional calculations
performed in the Kruskal coordinates. We resolve this conflict by invoking that
the Kruskcal coordinates could be no longer proper coordinates at the horizon.
In the Hartle-Hawking-Israel state, despite the negative finite proper energy
density at the horizon, the Tolman temperature is divergent there due to the
infinite blueshift of the Hawking temperature. However, a consistent
Stefan-Boltzmann law with the Hawking radiation shows that the effective Tolman
temperature is eventually finite everywhere and the equivalence principle is
surprisingly restored at the horizon. Then, we also show that the firewall
necessarily emerges out of the Unruh vacuum, so that the Tolman temperature in
the evaporating black hole is naturally divergent due to the infinitely
blueshifted negative ingoing flux crossing the horizon, whereas the outgoing
Hawking radiation characterized by the effective Tolman temperature indeed
originates from the quantum atmosphere, not just at the horizon. So, the
firewall and the atmosphere for the Hawking radiation turn out to be
compatible, once we discard the fact that the Hawking radiation in the Unruh
state originates from the infinitely blueshifted outgoing excitations at the
horizon. Finally, as a cosmological application, the initial radiation energy
density in warm inflation scenarios has been assumed to be finite when
inflation starts. We successfully find the origin of the non-vanishing initial
radiation energy density in the warm inflation by using the effective Tolman
temperature. | gr-qc |
Hawking radiation from nonrotating singularity-free black holes in
conformal gravity: We study the sparsity of Hawking radiation from nonrotating singularity-free
black holes in conformal gravity. We give a rigorous bound on the greybody
factor for massless scalar field and calculate the sparsity of Hawking
radiation from the black hole. Besides, we investigate the dependence of the
greybody factor and the sparsity of Hawking radiation on the conformal
parameters. Our study shows that the Hawking radiation from the black hole is
extremely sparse. When the conformal parameters are large, the increase of
conformal parameters will lead to an even more sparse Hawking radiation, while
to a less sparse Hawking radiation if the conformal parameters are small. | gr-qc |
Dynamical model for primordial black holes: Primordial black holes are analytically and numerically discussed based on
the extended McVittie spacetime solution. By assuming that dark matter and
radiation are the only sources of energy accreted by the forming central
object, it is found that the black-hole mass evolution depends on the initial
mass of the seed, the time in which the black hole emerges, and also on the
average peculiar velocity of dark matter particles. Constraints on the initial
conditions of the primordial black holes are derived from profiles of the
black-hole accretion mechanism and cosmological environment. A large range of
masses is compatible with our approach. In particular, masses of the order of
$10^{10}M_{\odot}$ today may also be generated from small seeds. An incubation
time for the emerging horizons is observed when the initial masses of the seeds
are close to the particle-horizon mass. It is also argued that the
McVittie-type description is consistent with the Schwarzschild solution as long
as other astrophysical processes near the central object are neglected. | gr-qc |
Late vacuum choice and slow roll approximation in gravitational particle
production during reheating: In the transition between inflation and reheating, the curvature scalar
typically undergoes oscillations which have significant impact on the density
of gravitationally produced particles. The commonly used adiabatic vacuum
prescription for the extraction of produced particle spectra becomes a
non-reliable definition of vacuum in the regimes for which this oscillatory
behavior is important. In this work, we study particle production for a scalar
field non-minimally coupled to gravity, taking into account the complete
dynamics of spacetime during inflation and reheating. We derive an
approximation for the solution to the mode equation during the slow-roll of the
inflaton and analyze the importance of Ricci scalar oscillations in the
resulting spectra. Additionally, we propose a prescription for the vacuum that
allows to safely extrapolate the result to the present, given that the test
field interacts only gravitationally. Lastly, we calculate the abundance of
dark matter this mechanism yields and compare it to observations. | gr-qc |
All-sky search for periodic gravitational waves in LIGO S4 data: We report on an all-sky search with the LIGO detectors for periodic
gravitational waves in the frequency range 50-1000 Hz and with the frequency's
time derivative in the range -1.0E-8 Hz/s to zero. Data from the fourth LIGO
science run (S4) have been used in this search. Three different semi-coherent
methods of transforming and summing strain power from Short Fourier Transforms
(SFTs) of the calibrated data have been used. The first, known as "StackSlide",
averages normalized power from each SFT. A "weighted Hough" scheme is also
developed and used, and which also allows for a multi-interferometer search.
The third method, known as "PowerFlux", is a variant of the StackSlide method
in which the power is weighted before summing. In both the weighted Hough and
PowerFlux methods, the weights are chosen according to the noise and detector
antenna-pattern to maximize the signal-to-noise ratio. The respective
advantages and disadvantages of these methods are discussed. Observing no
evidence of periodic gravitational radiation, we report upper limits; we
interpret these as limits on this radiation from isolated rotating neutron
stars. The best population-based upper limit with 95% confidence on the
gravitational-wave strain amplitude, found for simulated sources distributed
isotropically across the sky and with isotropically distributed spin-axes, is
4.28E-24 (near 140 Hz). Strict upper limits are also obtained for small patches
on the sky for best-case and worst-case inclinations of the spin axes. | gr-qc |
Analytical model of strange star in the low-mass X-ray binary 4U 1820-30: In this article, we have proposed a model for a realistic strange star under
Tolman VII metric\citep{Tolman1939}. Here the field equations are reduced to a
system of three algebraic equations for anisotropic pressure. Mass, central
density and surface density of strange star in the low-mass X-ray binary 4U
1820-30 has been matched with the observational data according to our model.
Strange materials clearly satisfies the stability condition (i.e. sound
velocities < 1) and TOV-equation. Here also surface red shift of the star has
been found to be within reasonable limit. | gr-qc |
Schwarzschild metrics and quasi-universes: The exterior and interior Schwarzschild solutions are rewritten replacing the
usual radial variable with an angular one. This allows to obtain some results
otherwise less apparent or even hidden in other coordinate systems. | gr-qc |
A Hairy Box in Three Dimensions: In this short note, we consider the phases of gravity coupled to a $U(1)$
gauge field and charged scalar in 2+1 dimensions without a cosmological
constant, but with box boundary conditions. This is an extension of the results
in arXiv:1609.01208, but unlike in higher dimensions, here the physics has
sharp differences from the corresponding AdS problem. This is because
Einstein-Maxwell black holes cease to exist when the cosmological constant goes
to zero. We show that hairy black holes also do not exist in the flat 2+1
dimensional box under some assumptions, but hairy boson stars do. There is a
second order phase transition from the empty box to the boson star phase at a
charge density larger than some critical value. We find various new features in
the phase diagram which were absent in 3+1 dimensions. Our explicit
calculations assume radial symmetry, but we also note that the absence of black
holes is more general. It is a trivial consequence of a 2+1 dimensional version
of Hawking's horizon topology argument from 3+1 dimensions, and relies on the
Dominant Energy Condition, which is violated when (eg.) there is a negative
cosmological constant. | gr-qc |
Is thermodynamics of the universe bounded by the event horizon a
Bekenstein system?: In this brief communication, we have studied the validity of the first law of
thermodynamics for the universe bounded by event horizon with two examples. The
key point is the appropriate choice of the temperature on the event horizon.
Finally, we have concluded that universe bounded by the event horizon may be a
Bekenstein system and the Einstein's equations and the first law of
thermodynamics on the event horizons are equivalent. | gr-qc |
Anomalous Lense-Thirring precession in Kerr-Taub-NUT spacetimes: Exact Lense-Thirring (LT) precession in Kerr-Taub-NUT spacetime is reviewed.
It is shown that the LT precession does not obey the general inverse cube law
of distance at strong gravity regime in Kerr-Taub-NUT spacetime. Rather, it
becomes maximum just near the horizon, falls sharply and becomes zero near the
horizon. The precession rate increases again and after that it falls obeying
the general inverse cube law of distance. This anomaly is maximum at the polar
region of this spacetime and it vanishes after crossing a certain `critical'
angle towards equator from pole. We highlight that this particular `anomaly'
also arises in the LT effect at the interior spacetime of the pulsars and such
a signature could be used to identify a role of Taub-NUT solutions in the
astrophysical observations or equivalently, a signature of the existence of NUT
charge in the pulsars. In addition, we show that if the Kerr-Taub-NUT spacetime
rotates with the angular momentum $J=Mn$ (Mass$\times$Dual Mass), inner horizon
goes to at $r=0$ and only {\it event horizon} exists at the distance $r=2M$. | gr-qc |
Magnetic and Electric Black Holes in the Vector-Tensor Horndeski Theory: We construct exact solutions of magnetically charged black holes in the
vector-tensor Horndeski gravity and discuss their main features. Unlike the
analogous electric case, the field equations are linear in a simple (quite
standard) parametrization of the metric tensor and they can be solved
analytically even when a cosmological constant is added. The solutions are
presented in terms of hypergeometric functions which makes the analysis of the
black hole properties relatively straightforward. Some of the aspects of these
black holes are quite ordinary like the existence of extremal configurations
with maximal magnetic charge for a given mass, or the existence of a mass with
maximal temperature for a given charge, but others are somewhat unexpected,
like the existence of black holes with a repulsive gravitational field. We
perform our analysis for both signs of the non-minimal coupling constant and
find black hole solutions in both cases but with significant differences
between them. The most prominent difference is the fact that the black holes
for the negative coupling constant have a spherical surface of curvature
singularity rather than a single point. On the other hand, the gravitational
field produced around this kind of black holes is always attractive. Also, for
small enough magnetic charge and negative coupling constant, extremal black
holes do not exist and all magnetic black holes have a single horizon. In
addition we study the trajectories around these magnetic black holes for light
as well as massive particles either neutral or electrically charged. Finally,
we compare the main features of these black holes with their electric
counterparts, adding some aspects that have not been discussed before, like
temperature, particle trajectories and light deflection by electrically charged
Horndesky black holes. | gr-qc |
Spin-Gravity Coupling: Mathisson's spin-gravity coupling and its Larmor-equivalent interaction,
namely, the spin-rotation coupling are discussed. The study of the latter leads
to a critical examination of the basic role of locality in relativistic
physics. The nonlocal theory of accelerated systems is outlined and some of its
implications are described. | gr-qc |
Dynamical shift conditions for the Z4 and BSSN hyperbolic formalisms: A class of dynamical shift conditions is shown to lead to a strongly
hyperbolic evolution system, both in the Z4 and in the BSSN Numerical
Relativity formalisms. This class generalizes the harmonic shift condition,
where light speed is the only non-trivial characteristic speed, and it is
contained into the multi-parameter family of minimal distortion shift
conditions recently proposed by Lindblom and Scheel. The relationship with the
analogous 'dynamical freezing' shift conditions used in black hole simulations
discussed. | gr-qc |
A method for calculating the imaginary part of the Hadamard Elementary
function $G^{(1)}$ in static, spherically symmetric spacetimes: Whenever real particle production occurs in quantum field theory, the
imaginary part of the Hadamard Elementary function $G^{(1)}$ is non-vanishing.
A method is presented whereby the imaginary part of $G^{(1)}$ may be calculated
for a charged scalar field in a static spherically symmetric spacetime with
arbitrary curvature coupling and a classical electromagnetic field $A^{\mu}$.
The calculations are performed in Euclidean space where the Hadamard Elementary
function and the Euclidean Green function are related by $(1/2)G^{(1)}=G_{E}$.
This method uses a $4^{th}$ order WKB approximation for the Euclideanized mode
functions for the quantum field. The mode sums and integrals that appear in the
vacuum expectation values may be evaluated analytically by taking the large
mass limit of the quantum field. This results in an asymptotic expansion for
$G^{(1)}$ in inverse powers of the mass $m$ of the quantum field.
Renormalization is achieved by subtracting off the terms in the expansion
proportional to nonnegative powers of $m$, leaving a finite remainder known as
the ``DeWitt-Schwinger approximation.'' The DeWitt-Schwinger approximation for
$G^{(1)}$ presented here has terms proportional to both $m^{-1}$ and $m^{-2}$.
The term proportional to $m^{-2}$ will be shown to be identical to the
expression obtained from the $m^{-2}$ term in the generalized DeWitt-Schwinger
point-splitting expansion for $G^{(1)}$. The new information obtained with the
present method is the DeWitt-Schwinger approximation for the imaginary part of
$G^{(1)}$, which is proportional to $m^{-1}$ in the DeWitt-Schwinger
approximation for $G^{(1)}$ derived in this paper. | gr-qc |
About Torsional Weyl-Dirac Electrodynamics: A classical general relativistic theory possessing magnetic currents, as well
electric ones and admitting massive photons was built up. As the geometric
basis serves a space with Weylian non-metricity and torsion. The theory is
coordinate covariant as well Weyl-gauge covariant. In the limit one obtains the
ordinary Einstein-Maxwell theory. | gr-qc |
Generation of inflationary perturbations in the continuous spontaneous
localization model: The second order power spectrum: Cosmic inflation, which describes an accelerated expansion of the early
Universe, yields the most successful predictions regarding temperature
anisotropies in the cosmic microwave background (CMB). Nevertheless, the
precise origin of the primordial perturbations and their quantum-to-classical
transition is still an open issue. The continuous spontaneous localization
model (CSL), in the cosmological context, might be used to provide a solution
to the mentioned puzzles by considering an objective reduction of the inflaton
wave function. In this work, we calculate the primordial power spectrum at the
next leading order in the Hubble flow functions that results from applying the
CSL model to slow roll inflation within the semiclassical gravity framework. We
employ the method known as uniform approximation along with a second order
expansion in the Hubble flow functions. We analyze some features in the CMB
temperature and primordial power spectra that could help to distinguish between
the standard prediction and our approach. | gr-qc |
Noncommutative Effective LQC: inclusion of potential term: We construct and study a simple noncommutative scheme (theta-deformation) for
the effective Loop Quantum Cosmology of the flat
Friedmann-Lema\^itre-Robertson-Walker model in the presence of a homogeneous
scalar field $\phi$ with a potential $\mathcal{V}(\phi)=\frac{1}{2}m^2\phi^2$.
We first conduct a simple analysis from the corresponding Hamilton equations of
motion considering a generic term $\mathcal V(\phi)$. It is observed that the
characteristic Big Bounce of Loop Quantum Cosmology is preserved under such
noncommutative extension. When specializing to the quadratic case, numerical
solutions to the corresponding Hamilton equations exhibiting an early
inflationary epoch with a sufficiently large number of e-foldings are found. It
is concluded that, in this noncommutative setup, solutions exist which are in
the overall compatible with the early universe predicted by standard
(effective) Loop Quantum Cosmology (i.e. a bouncing and inflationary early
universe). The issue of the genericness of a sufficiently long inflationary
period on the space of solutions in this noncommutative construct remains to be
addressed. | gr-qc |
Stellar equilibrium in Einstein-Chern-Simons gravity: We consider a spherically symmetric internal solution within the context of
Einstein-Chern-Simons gravity and derive a generalized five-dimensional
Tolman-Oppenheimer-Volkoff (TOV) equation. It is shown that the generalized TOV
equation leads, in a certain limit, to the standard five-dimensional TOV
equation | gr-qc |
Quintessence, the Gravitational Constant, and Gravity: Dynamical vacuum energy or quintessence, a slowly varying and spatially
inhomogeneous component of the energy density with negative pressure, is
currently consistent with the observational data. One potential difficulty with
the idea of quintessence is that couplings to ordinary matter should be
strongly suppressed so as not to lead to observable time variations of the
constants of nature. We further explore the possibility of an explicit coupling
between the quintessence field and the curvature. Since such a scalar field
gives rise to another gravity force of long range ($\simg H^{-1}_0$), the solar
system experiments put a constraint on the non-minimal coupling: $|\xi| \siml
10^{-2}$. | gr-qc |
Observing dynamic oscillatory behavior of triple points among black hole
thermodynamic phase transitions: Understanding the dynamic process of black hole thermodynamic phase
transitions at a triple point is a huge challenge. In this letter, we carry out
the first investigation of dynamical phase behaviour at a black hole triple
point. By numerically solving the Smoluchowski equation near the triple point
for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we find
that initial small, intermediate, or large black holes can transit to the other
two coexistent phases at the triple point, indicating that thermodynamic phase
transitions can indeed occur dynamically. More significantly, we observe
characteristic weak and strong oscillatory behaviour in this dynamic process,
which can be understood from an investigation of the rate of first passage from
one phase to another. Our results further an understanding of the dynamic
process of black hole thermodynamic phase transitions. | gr-qc |
High energy particle collisions and geometry of horizon: We consider collision of two geodesic particles near the horizon of such an
axially symmetric black hole (rotating or static) that the metric coefficient
$g_{\phi \phi }\rightarrow 0$ there. It is shown that (both for regular and
singular horizons) the energy in the centre of mass frame $% E_{c.m.}$ is
indefinitely large even without fine-tuning of particles' parameters.
Kinematically, this is collision between two rapid particles that approach the
horizon almost with the speed of light but at different angles. The latter is
the reason why the relative velocity tends to that of light, hence to high
$E_{c.m.}$. Our approach is model-independent. It relies on general properties
of geometry and is insensitive to the details of material source that supports
the geometies of the type under consideration. For several particular models
(the stringy black hole, the Brans-Dicke analogue of the Schwarzschild metric
and the Janis-Newman-Winicour one) we recover the results found in literature
previously. | gr-qc |
Compatibility complexes of overdetermined PDEs of finite type, with
applications to the Killing equation: In linearized gravity, two linearized metrics are considered
gauge-equivalent, $h_{ab} \sim h_{ab} + K_{ab}[v]$, when they differ by the
image of the Killing operator, $K_{ab}[v] = \nabla_a v_b + \nabla_b v_a$. A
universal (or complete) compatibility operator for $K$ is a differential
operator $K_1$ such that $K_1 \circ K = 0$ and any other operator annihilating
$K$ must factor through $K_1$. The components of $K_1$ can be interpreted as a
complete (or generating) set of local gauge-invariant observables in linearized
gravity. By appealing to known results in the formal theory of overdetermined
PDEs and basic notions from homological algebra, we solve the problem of
constructing the Killing compatibility operator $K_1$ on an arbitrary
background geometry, as well as of extending it to a full compatibility complex
$K_i$ ($i\ge 1$), meaning that for each $K_i$ the operator $K_{i+1}$ is its
universal compatibility operator. Our solution is practical enough that we
apply it explicitly in two examples, giving the first construction of full
compatibility complexes for the Killing operator on these geometries. The first
example consists of the cosmological FLRW spacetimes, in any dimension. The
second consists of a generalization of the Schwarzschild-Tangherlini black hole
spacetimes, also in any dimension. The generalization allows an arbitrary
cosmological constant and the replacement of spherical symmetry by planar or
pseudo-spherical symmetry. | gr-qc |
Model-independent test of the parity symmetry of gravity with
gravitational waves: Gravitational wave (GW) data can be used to test the parity symmetry of
gravity by investigating the difference between left-hand and right-hand
circular polarization modes. In this article, we develop a method to decompose
the circular polarizations of GWs produced during the inspiralling stage of
compact binaries, with the help of stationary phase approximation. The foremost
advantage is that this method is simple, clean, independent of GW waveform, and
is applicable to the existing detector network. Applying it to the mock data,
we test the parity symmetry of gravity by constraining the velocity
birefringence of GWs. If a nearly edge-on binary neutron-stars with observed
electromagnetic counterparts at 40 Mpc is detected by the second-generation
detector network, one could derive the model-independent test on the parity
symmetry in gravity: the lower limit of the energy scale of parity violation
can be constrained within $\mathcal{O}(10^4{\rm eV})$. | gr-qc |
On Challenges to Separability of the Dirac Equation in Kerr Geometry
under Compact Hyperboloidal Coordinates: The Dirac equation governs the behaviour of spin-1/2 particles. The
equation's separability into decoupled radial and angular differential
equations is a crucial step in analytical and numerical computations of
quantities like eigenvalues, quasinormal modes and bound states. However, this
separation has been performed in co-ordinate systems that are not well-behaved
in either limiting regions of $r \rightarrow r_{horizon}$, $r \rightarrow
r_\infty$ or both. In particular, the extensively used Boyer-Lindquist
co-ordinates contains unphysical features of spacetime geometry for both
$r_{horizon}$ and $r_\infty$. Therefore, motivated by the recently developed
compact hyperboloidal co-ordinate system for Kerr Black Holes that is well
behaved in these limiting regions, we attempt the separation of the Dirac
equation. We first construct a null tetrad suitable for the separability
analysis under the Newman-Penrose formalism. Then, an unexpected result is
shown that by using the standard separability procedure based on the mode
ansatz under this tetrad, the Dirac equation does not decouple into radial and
angular equationsPossible reasons for this behaviour as well as importance of
proving separability for various computations are discussed. | gr-qc |
Non-Canonical Inflation and Primordial Black Holes Production: We study a mechanism for the amplification of the inflationary scalar
perturbation when the inflaton field action is non-canonical, i.e. the inflaton
kinetic term has a non-standard form. For such a case the speed of sound of the
perturbations generated during inflation is less than one and in general
changes with time. Furthermore in such models, even when the scalar field
potential is negligible, diverse inflationary attractors may exist. The
possible effects of a speed of sound approaching zero during some stage of
inflation may lead to a large amplification for the amplitude of the scalar
spectrum which, on horizon re-entry during the radiation dominated phase, can
collapse and form primordial black holes (PBH) of a mass $M_{\rm BH}\sim
10^{-15}M_{\odot}$ which may constitute a large fraction of the total Dark
Matter (DM) today. | gr-qc |
The coincidence problem in the scenario of dark energy interacting with
two fluids: A cosmological model of dark energy interacting with dark matter and another
general component of the universe is considered. The evolution equations for
coincidence parameters r and s, which represent the ratios between the dark
energy and the matter and the other cosmic fluid, respectively, are analyzed in
terms of the stability of stationary solutions. The obtained general results
allow to shed some light on the coincidence problem and in the equations of
state of the three interacting fluids, due to the constraints imposes by the
stability of the solutions. We found that for an interaction proportional to
the sum of the DE density and the third fluid density, the hypothetical fluid
must have positive pressure, which leads naturally to a cosmological scenario
with radiation, unparticle or even some form of warm DM as the third
interacting fluid. | gr-qc |
Example of a stable wormhole in general relativity: We study a static, spherically symmetric wormhole model whose metric
coincides with that of the so-called Ellis wormhole but the material source of
gravity consists of a perfect fluid with negative density and a source-free
radial electric or magnetic field. For a certain class of fluid equations of
state, it has been shown that this wormhole model is linearly stable under both
spherically symmetric perturbations and axial perturbations of arbitrary
multipolarity. A similar behavior is predicted for polar nonspherical
perturbations. It thus seems to be the first example of a stable wormhole model
in the framework of general relativity (at least without invoking phantom thin
shells as wormhole sources). | gr-qc |
The Relativistic Transformation to Rotating Frames: We present a critical review of the relativistic rotation transformation of
Trocheris and Takeno. A new transformation is proposed which is free from the
drawbacks of the former. Some applications are presented. | gr-qc |
Gravitational Perturbation in Nonlocal Modified Tolman VII Model: In comparison to the original Tolman VII model, Exact Modified Tolman VII
(EMTVII) with one additional parameter can increase the compactness of compact
object. When the compactness is in the ultracompact regime, the quasinormal
modes~(QNMs) of the trapped mode as well as the gravitational echoes become
more viable. Starting with the EMTVII model, we introduce nonlocality into the
matter sector and analyze the effective potential, the QNMs, and the
gravitational echoes of the compact and ultracompact object in the nonlocal
model. The nonlocal gravity version of EMTVII~(NEMTVII) is parametrized by the
nonlocal parameter~($ \beta $), modified Tolman VII parameter ($ \alpha $), and
the compactness ($ \mathcal{C}$). It is found that the nonlocal profile
produces the smeared surface and consequently reduce the compactness. The
maximum compactness $\mathcal{C}_{max}=0.4$ occurs when $\alpha=0=\beta$, i.e.,
EMTVII with no smearing. For relatively small value of $\beta = 0.01$ and the
compactness $ \mathcal{C} \lesssim 0.2667$~(with $M=2.14$ solar masses,
$R=11.835$ km at $\alpha=1.4$), the causality condition and the dominant energy
condition~(DEC) are satisfied. The quasinormal modes of the gravitational
perturbation are calculated using Bohr-Sommerfeld (BS) fitting and we find that
the nonlocality produces less trapped modes than the original (EMTVII)
counterpart. At high compactness, gravitational echoes are simulated
numerically. Echoes are found to exist in the parameter space where the
dominant energy condition and the causality condition are violated. | gr-qc |
Cosmological Evolution of Pilgrim Dark Energy: We study pilgrim dark energy model by taking IR cut-offs as particle and
event horizons as well as conformal age of the universe. We derive evolution
equations for fractional energy density and equation of state parameters for
pilgrim dark energy. The phantom cosmic evolution is established in these
scenarios which is well supported by the cosmological parameters such as
deceleration parameter, statefinder parameters and phase space of
$\omega_\vartheta$ and $\omega'_\vartheta$. We conclude that the consistent
value of parameter $\mu$ is $\mu<0$ in accordance with the current Planck and
WMAP$9$ results. | gr-qc |
Curvature dark energy reconstruction through different cosmographic
distance definitions: In the context of $f(\mathcal{R})$ gravity, dark energy is a geometrical
fluid with negative equation of state. Since the function $f(\mathcal{R})$ is
not known \emph{a priori}, the need of a model independent reconstruction of
its shape represents a relevant technique to determine which $f(\mathcal{R})$
model is really favored with respect to others. To this aim, we relate
cosmography to a generic $f(\mathcal R)$ and its derivatives in order to
provide a model independent investigation at redshift $z \sim 0$. Our analysis
is based on the use of three different cosmological distance definitions, in
order to alleviate the duality problem, i.e. the problem of which cosmological
distance to use with specific cosmic data sets. We therefore consider the
luminosity, $d_L$, flux, $d_F$, and angular, $d_A$, distances and we find
numerical constraints by the Union 2.1 supernovae compilation and measurement
of baryonic acoustic oscillations, at $z_{BAO}=0.35$. We notice that all
distances reduce to the same expression, i.e. $d_{L;F;A}\sim\frac{1}{\mathcal
H_0}z$, at first order. Thus, to fix the cosmographic series of observables, we
impose the initial value of $H_0$ by fitting $\mathcal H_0$ through supernovae
only, in the redshift regime $z<0.4$. We find that the pressure of curvature
dark energy fluid is slightly lower than the one related to the cosmological
constant. This indicates that a possible evolving curvature dark energy
realistically fills the current universe. Moreover, the combined use of
$d_L,d_F$ and $d_A$ shows that the sign of the acceleration parameter agrees
with theoretical bounds, while its variation, namely the jerk parameter, is
compatible with $j_0>1$. Finally, we infer the functional form of
$f(\mathcal{R})$ by means of a truncated polynomial approximation, in terms of
fourth order scale factor $a(t)$. | gr-qc |
Quantum-wave equation and Heisenberg inequalities of covariant quantum
gravity: Key aspects of the manifestly-covariant theory of quantum gravity
(Cremaschini and Tessarotto 2015-2017) are investigated. These refer, first, to
the establishment of the 4-scalar, manifestly-covariant evolution quantum wave
equation, denoted as covariant quantum gravity (CQG) wave equation, which
advances the quantum state $\psi $ associated with a prescribed background
space-time. In this paper, the CQG-wave equation is proved to follow at once by
means of a Hamilton-Jacobi quantization of the classical variational tensor
field $g\equiv \left\{ g_{\mu \nu }\right\} $ and its conjugate momentum,
referred to as (canonical) $g-$quantization. The same equation is also shown to
be variational and to follow from a synchronous variational principle
identified here with the quantum Hamilton variational principle. The
corresponding quantum hydrodynamic equations are then obtained upon introducing
the Madelung representation for $\psi $, which provide an equivalent
statistical interpretation of the CQG-wave equation. Finally, the quantum state
$\psi $ is proved to fulfill generalized Heisenberg inequalities, relating the
statistical measurement errors of quantum observables. These are shown to be
represented in terms of the standard deviations of the matric tensor $g\equiv
\left\{ g_{\mu \nu }\right\} $ and its quantum conjugate momentum operator. | gr-qc |
Virial identities in relativistic gravity: 1D effective actions and the
role of boundary terms: Virial (aka scaling) identities are integral identities that are useful for a
variety of purposes in non-linear field theories, including establishing no-go
theorems for solitonic and black hole solutions, as well as for checking the
accuracy of numerical solutions. In this paper, we provide a pedagogical
rationale for the derivation of such integral identities, starting from the
standard variational treatment of particle mechanics. In the framework of
one-dimensional (1D) effective actions, the treatment presented here yields a
set of useful formulas for computing virial identities in any field theory.
Then, we propose that a complete treatment of virial identities in relativistic
gravity must take into account the appropriate boundary term. For General
Relativity this is the Gibbons-Hawking-York boundary term. We test and confirm
this proposal with concrete examples. Our analysis here is restricted to
spherically symmetric configurations, which yield 1D effective actions (leaving
higher-D effective actions and in particular the axially symmetric case to a
companion paper). In this case, we show that there is a particular "gauge"
choice, $i.e.$ a choice of coordinates and parameterizing metric functions,
that simplifies the computation of virial identities in General Relativity,
making both the Einstein-Hilbert action and the Gibbons-Hawking-York boundary
term non-contributing. Under this choice, the virial identity results
exclusively from the matter action. For generic "gauge" choices, however, this
is not the case. | gr-qc |
How to tell a gravastar from a black hole: Gravastars have been recently proposed as potential alternatives to explain
the astrophysical phenomenology traditionally associated to black holes,
raising the question of whether the two objects can be distinguished at all.
Leaving aside the debate about the processes that would lead to the formation
of a gravastar and the astronomical evidence in their support, we here address
two basic questions: Is a gravastar stable against generic perturbations? If
stable, can an observer distinguish it from a black hole of the same mass? To
answer these questions we construct a general class of gravastars and determine
the conditions they must satisfy in order to exist as equilibrium solutions of
the Einstein equations. For such models we perform a systematic stability
analysis against axial-perturbations, computing the real and imaginary parts of
the eigenfrequencies. Overall, we find that gravastars are stable to axial
perturbations, but also that their quasi-normal modes differ from those of a
black hole of the same mass and thus can be used to discern, beyond dispute, a
gravastar from a black hole. | gr-qc |
Rotation of polarization by a moving gravitational lens: We present a simple prescription for the rotation of polarization produced by
a relativistically moving gravitational lens, applicable to arbitrary
deflection angle and arbitrary velocity of the lens. When geometric optics is
applicable, two independent components contribute to the total rotation of
polarization: (i) in the frame of the lens the polarization vector experiences
minimal rotation defined by the deflection angle (as measured by a set of
remote observers, or no rotation if defined in terms of parallel-propagated
tetrad); (ii) the effect of the motion of the lens on the polarization can be
taken into account exactly using special relativistic Lorentz transformation of
polarization. The effects of the gravitational lensing are thus parametrized by
the deflection angle of the null geodesics (not necessarily small) and the
motion of the lens (not necessarily with velocities much smaller than that of
light). | gr-qc |
On the stability and deformability of top stars: Topological stars, or top stars for brevity, are smooth horizonless static
solutions of Einstein-Maxwell theory in 5-d that reduce to spherically
symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear
scalar perturbations of top stars and argue for their stability and
deformability. We tackle the problem with different techniques including WKB
approximation, numerical analysis, Breit-Wigner resonance method and quantum
Seiberg-Witten curves. We identify three classes of quasi-normal modes
corresponding to prompt-ring down modes, long-lived meta-stable modes and what
we dub `blind' modes. All mode frequencies we find have negative imaginary
parts, thus suggesting linear stability of top stars. Moreover we determine the
tidal Love and dissipation numbers encoding the response to tidal deformations
and, similarly to black holes, we find zero value in the static limit but,
contrary to black holes, we find non-trivial dynamical Love numbers and
vanishing dissipative effects at linear order. For the sake of illustration in
a simpler context, we also consider a toy model with a piece-wise constant
potential and a centrifugal barrier that captures most of the above features in
a qualitative fashion. | gr-qc |
Hayward black hole in scalar-Einstein-Gauss-Bonnet gravity in four
dimensions: In the framework of scalar-Einstein-Gauss-Bonnet gravity, we construct the
model which realizes the Hayward black hole and discuss the absence of ghosts
in this model. Because Hayward black hole has two horizons but no curvature
singularity, it may solve the problem of the information loss that might be
generated by black holes. The Gauss-Bonnet term appears as a stringy
correction, and therefore, our results might indicate that the stringy
correction would solve the information loss problem. | gr-qc |
Some new perspectives on the Kruskal--Szekeres extension with
applications to photon surfaces: It is a well-known fact that the Schwarzschild spacetime admits a maximal
spacetime extension in null coordinates which extends the exterior
Schwarzschild region past the Killing horizon, called the Kruskal-Szekeres
extension. This method of extending the Schwarzschild spacetime was later
generalized by Brill-Hayward to a class of spacetimes of "profile $h$" across
non-degenerate Killing horizons. Circumventing analytical subtleties in their
approach, we reconfirm this fact by reformulating the problem as an ODE, and
showing that the ODE admits a solution if and only if the naturally arising
Killing horizon is non-degenerate. Notably, this approach lends itself to
discussing regularity across the horizon for non-smooth metrics.
We will discuss applications to the study of photon surfaces, extending
results by Cederbaum-Galloway and Cederbaum-Jahns-Vi\v{c}\'{a}nek-Mart\'{i}nez
beyond the Killing horizon. In particular, our analysis asserts that photon
surfaces approaching the Killing horizon must necessarily cross it. | gr-qc |
The Closed String Tachyon and its relationship with the evolution of the
Universe: We present a cosmological landscape where the classical closed string tachyon
field plays an important role in the framework of a critical bosonic
compactification. Our cosmological solutions for a universe with constant
curvature describes an finite inflationary stage which expands till a maximum
value before undergoes a big crunch as the tachyon reaches the minimum of its
potential. | gr-qc |
Scalar polarization window in gravitational-wave signals: Scalar polarization modes of gravitational waves, which are often introduced
in the context of the viable extension of gravity, have been actively searched.
However, couplings of the scalar modes to the matter are strongly constrained
by the fifth-force experiments. Thus, the amplitude of scalar polarization in
the observed gravitational-wave signal must be significantly suppressed
compared to that of the tensor modes. Here, we discuss the implications of the
experiments in the solar system on the detectability of scalar modes in
gravitational waves from compact binary coalescences, taking into account the
whole processes from the generation to the observation of gravitational waves.
We first claim that the energy carried by the scalar modes at the generation
is, at most, that of the tensor modes from the observed phase evolution of the
inspiral gravitational waves. Next, we formulate general gravitational-wave
propagation and point out that the energy flux hardly changes through
propagation as long as the background changes slowly compared to the wavelength
of the propagating waves. Finally, we show that the possible magnitude of
scalar polarization modes detected by the ground-based gravitational-wave
telescopes is already severely constrained by the existing gravity tests in the
solar system. | gr-qc |
Isotropic Loop Quantum Cosmology with Matter: A free massless scalar field is coupled to homogeneous and isotropic loop
quantum cosmology. The coupled model is investigated in the vicinity of the
classical singularity, where discreteness is essential and where the quantum
model is non-singular, as well as in the regime of large volumes, where it
displays the expected semiclassical features. The particular matter content
(massless, free scalar) is chosen to illustrate how the discrete structure
regulates pathological behavior caused by kinetic terms of matter Hamiltonians
(which in standard quantum cosmology lead to wave functions with an infinite
number of oscillations near the classical singularity). Due to this
modification of the small volume behavior the dynamical initial conditions of
loop quantum cosmology are seen to provide a meaningful generalization of
DeWitt's initial condition. | gr-qc |
Progress in Establishing a Connection Between the Electromagnetic
Zero-Point Field and Inertia: We report on the progress of a NASA-funded study being carried out at the
Lockheed Martin Advanced Technology Center in Palo Alto and the California
State University in Long Beach to investigate the proposed link between the
zero-point field of the quantum vacuum and inertia. It is well known that an
accelerating observer will experience a bath of radiation resulting from the
quantum vacuum which mimics that of a heat bath, the so-called Davies-Unruh
effect. We have further analyzed this problem of an accelerated object moving
through the vacuum and have shown that the zero-point field will yield a
non-zero Poynting vector to an accelerating observer. Scattering of this
radiation by the quarks and electrons constituting matter would result in an
acceleration-dependent reaction force that would appear to be the origin of
inertia of matter (Rueda and Haisch 1998a, 1998b). In the subrelativistic case
this inertia reaction force is exactly newtonian and in the relativistic case
it exactly reproduces the well known relativistic extension of Newton's Law.
This analysis demonstrates then that both the ordinary, F=ma, and the
relativistic forms of Newton's equation of motion may be derived from Maxwell's
equations as applied to the electromagnetic zero-point field. We expect to be
able to extend this analysis in the future to more general versions of the
quantum vacuum than just the electromagnetic one discussed herein. | gr-qc |
A Summary: Quantum Singularities in Static and Conformally Static
Spacetimes: This is a summary of how the definition of quantum singularity is extended
from static space-times to conformally static space-times. Examples are given. | gr-qc |
The Patchwork Divergence Theorem: The divergence theorem in its usual form applies only to suitably smooth
vector fields. For vector fields which are merely piecewise smooth, as is
natural at a boundary between regions with different physical properties, one
must patch together the divergence theorem applied separately in each region.
We give an elegant derivation of the resulting "patchwork divergence theorem"
which is independent of the metric signature in either region, and which is
thus valid if the signature changes.
(PACS numbers 4.20.Cv, 04.20.Me, 11.30.-j, 02.40.Hw) | gr-qc |
Quasinormal modes and Hawking radiation of black holes in cubic gravity: We consider quasinormal modes and Hawking radiation of four-dimensional
asymptotically flat black holes in the most general up
to-cubic-order-in-curvature dimension-independent Einsteinian theory of gravity
that shares its graviton spectrum with the Einstein theory on constant
curvature backgrounds. We show that damping rate and real oscillation
frequencies of quasinormal modes for scalar, electromagnetic and Dirac fields
are suppressed once the coupling with the cubic term is on. The intensity of
Hawking radiation is suppressed as well, leading to, roughly, one order longer
lifetime at a sufficiently large coupling constant. | gr-qc |
Numerical confirmations of joint spike transitions in $G_2$ cosmologies: We produce numerical evidence that the joint spike transitions between Kasner
eras of $G_2$ cosmologies are described by the non-orthogonally transitive
$G_2$ spike solution. A new matching procedure is developed for this purpose. | gr-qc |
Cosmology, cohomology, and compactification: Ashtekar and Samuel have shown that Bianchi cosmological models with compact
spatial sections must be of Bianchi class A. Motivated by general results on
the symmetry reduction of variational principles, we show how to extend the
Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as
defined, e.g., by Singer and Thurston. In particular, it is shown that any
m-dimensional homogeneous space G/K admitting a G-invariant volume form will
allow a compact discrete quotient only if the Lie algebra cohomology of G
relative to K is non-vanishing at degree m. | gr-qc |
LQG vertex with finite Immirzi parameter: We extend the definition of the "flipped" loop-quantum-gravity vertex to the
case of a finite Immirzi parameter. We cover the Euclidean as well as the
Lorentzian case. We show that the resulting dynamics is defined on a Hilbert
space isomorphic to the one of loop quantum gravity, and that the area operator
has the same discrete spectrum as in loop quantum gravity. This includes the
correct dependence on the Immirzi parameter, and, remarkably, holds in the
Lorentzian case as well. The ad hoc flip of the symplectic structure that was
initially required to derive the flipped vertex is not anymore needed for
finite Immirzi parameter. These results establish a bridge between canonical
loop quantum gravity and the spinfoam formalism in four dimensions. | gr-qc |
Perturbative deflection angle, gravitational lensing in the strong field
limit and the black hole shadow: A perturbative method to compute the deflection angle of both timelike and
null rays in arbitrary static and spherically symmetric spacetimes in the
strong field limit is proposed. The result takes a quasi-series form of
$(1-b_c/b)$ where $b$ is the impact parameter and $b_c$ is its critical value,
with coefficients of the series explicitly given. This result also naturally
takes into account the finite distance effect of both the source and detector,
and allows to solve the apparent angles of the relativistic images in a more
precise way. From this, the BH angular shadow size is expressed as a simple
formula containing metric functions and particle/photon sphere radius. The
magnification of the relativistic images were shown to diverge at different
values of the source-detector angular coordinate difference, depending on the
relation between the source and detector distance from the lens. To verify all
these results, we then applied them to the Hayward BH spacetime, concentrating
on the effects of its charge parameter $l$ and the asymptotic velocity $v$ of
the signal. The BH shadow size were found to decrease slightly as $l$ increase
to its critical value, and increase as $v$ decreases from light speed. For the
deflection angle and the magnification of the images however, both the increase
of $l$ and decrease of $v$ will increase their values. | gr-qc |
On the mass radiated by coalescing black-hole binaries: We derive an analytic phenomenological expression that predicts the final
mass of the black-hole remnant resulting from the merger of a generic binary
system of black holes on quasi-circular orbits. Besides recovering the correct
test-particle limit for extreme mass-ratio binaries, our formula reproduces
well the results of all the numerical-relativity simulations published so far,
both when applied at separations of a few gravitational radii, and when applied
at separations of tens of thousands of gravitational radii. These validations
make our formula a useful tool in a variety of contexts ranging from
gravitational-wave physics to cosmology. As representative examples, we first
illustrate how it can be used to decrease the phase error of the
effective-one-body waveforms during the ringdown phase. Second, we show that,
when combined with the recently computed self-force correction to the binding
energy of nonspinning black-hole binaries, it provides an estimate of the
energy emitted during the merger and ringdown. Finally, we use it to calculate
the energy radiated in gravitational waves by massive black-hole binaries as a
function of redshift, using different models for the seeds of the black-hole
population. | gr-qc |
Wormholes in String Theory: A wormhole is constructed by cutting and joining two spacetimes satisfying
the low energy string equations with a dilaton field. In spacetimes described
by the "string metric" the dilaton energy-momentum tensor need not satisfy the
weak or dominant energy conditions. In the cases considered here the dilaton
field violates these energy conditions and is the source of the exotic matter
required to maintain the wormhole. There is also a surface stress-energy, that
must be produced by additional matter, where the spacetimes are joined. It is
shown that wormholes can be constructed for which this additional matter
satisfies the weak and dominant energy conditions, so that it could be a form
of "normal" matter. Charged dilaton wormholes with a coupling between the
dilaton and the electromagnetic field that is more general than in string
theory are also briefly discussed. | gr-qc |
Van der Waals Universe with Adiabatic Matter Creation: A FRWL cosmological model with perfect fluid comprising of van der Waals gas
and dust has been studied in the context of dynamical analysis of a
three-component autonomous non-linear dynamical system for the particle number
density $n$, the Hubble parameter $H$, and the temperature $T$. Perfect fluid
isentropic particle creation at rate proportional to an integer power $\alpha$
of $H$ has been incorporated. The existence of a global first integral allows
the determination of the temperature evolution law and hence the reduction of
the dynamical system to a two-component one. Special attention is paid to the
cases of $\alpha = 2$ and $\alpha = 4$ and these are illustrated with numerical
examples. The global dynamics is comprehensively studied for different choices
of the values of the physical parameters of the model. Trajectories in the $(n,
H)$ phase space are identified for which temporary inflationary regime exists. | gr-qc |
A Note on Brane Inflation: We demonstrate that there exists an inflationary solution on the positive
tension brane in the Randall-Sundrum scenario. Inflation is driven by a
slow-rolling scalar field on the brane and is achieved within the perturbative
limit of the radion field. We find that inflation on the positive tension brane
results in a slight increase in the separation between the two branes. However,
we show that the slow-roll inflation is not possible on the negative tension
brane. | gr-qc |
Observational constraints on the Emergent Universe with interacting
non-linear fluids and its stability analysis: We investigate a flat Emergent Universe (EU) with a nonlinear equation of
state which is equivalent to three different compositions of fluids. In the EU,
initially, the evolution of the universe began with no interaction, but as time
evolves, an interaction sets in among the three fluids leading to the observed
universe. The characteristic of an EU is that it is a singularity-free universe
that evolves with all the basic features of the early evolution. A given
nonlinear equation of state parameter permits a universe with three different
fluids. We get a universe with dark energy, cosmic string, and radiation
domination to begin with, which at a later epoch transits into a universe with
three different fluids with matter domination, dark matter, and dark energy for
a given interaction strength among the cosmic fluids. Later the model
parameters are constrained using the observed Hubble data and Type Ia Supernova
(SnIa) data from the Pantheon data set. The classical stability analysis of the
model is performed using the square speed of sound. It is found that a
theoretically stable cosmological model can be obtained in this case, however,
the model becomes classically unstable at the present epoch when the
observational bounds on the model parameters are taken into account. | gr-qc |
Anisotropic neutron stars by gravitational decoupling: In this work we obtain an anisotropic neutron star solution by gravitational
decoupling starting from a perfect fluid configuration which has been used to
model the compact object PSR J0348+0432. Additionally, we consider the same
solution to model the Binary Pulsar SAX J1808.4-3658 and X-ray Binaries Her X-1
and Cen X-3 ones. We study the acceptability conditions and obtain that the
MGD--deformed solution obey the same physical requirements as its isotropic
counterpart. Finally, we conclude that the most stable solutions, according to
the adiabatic index and gravitational cracking criterion, are those with the
smallest compactness parameters, namely SAX J1808.4-3658 and Her X-1. | gr-qc |
Beyond the spontaneous scalarization: New fully nonlinear dynamical
mechanism for formation of scalarized black holes: In the present letter we show the existence of a fully nonlinear dynamical
mechanism for the formation of scalarized black holes which is different from
the spontaneous scalarization. We consider a class of scalar-Gauss-Bonnet
gravity theories within which no tachyonic instability can occur. Although the
Schwarzschild black holes are linearly stable against scalar perturbations, we
show dynamically that for certain choices of the coupling function they are
unstable against nonlinear scalar perturbations. This nonlinear instability
leads to the formation of new black holes with scalar hair. The fully nonlinear
and self-consistent study of the equilibrium black holes reveals that the
spectrum of solutions is more complicated and more than one scalarized branch
can exist. We have also considered classes of scalar-Gauss-Bonnet theories
where both the standard and the nonlinear scalarization can be present, and
they are smoothly connected that completes in an interesting way the picture of
black hole scalarization. The fully nonlinear (de)scalarization of a
Schwarzschild black hole will always happen with a jump because the stable
"scalarized branch" is not continuously connected to the Schwarzschild one that
can leave clear observational signatures. | gr-qc |
Braneworld gravastars admitting conformal motion: In this work, we study the Mazur and Mottola gravastar model within the
context of Randall-Sundrum II type braneworld scenario, based on the fact that
our four dimensional space-time is a three-brane, embedded in a five
dimensional bulk. We present exact solutions of the modified field equations in
each of the three regions making up the gravastar, namely, (I) the core, (II)
the shell, and (III) the vacuum exterior. The junction conditions at each
interface are fulfilled and we further explore interesting physical properties
such as length and energy and entropy of the spherical distribution. | gr-qc |
Hubble drift in Palatini $f(\mathcal{R})$-theories: In a Palatini $f(\mathcal{R})$-model, we define chonodynamical effects due to
the choice of atomic clocks as standard reference clocks and we develop a
formalism able to quantitatively separate them from the usual effective dark
sources one has in extended theories. We apply the formalism to Hubble drift
and briefly discuss the issue about the physical frame. In particular, we argue
that there is no physical frame in the sense one does different things in
different frames and that, in a sense, is the physical characteristic of
extended gravity. As an example, we discuss how Jordan frame may be well suited
to discuss cosmology, though it fails within the solar system. | gr-qc |
The classical essence of black hole radiation: We show that the mathematics of Hawking process can be interpreted
classically as the Fourier analysis of an exponentially redshifted wave mode
which scatters off the black hole and travels to infinity at late times. We use
this method to derive the Planckian power spectrum for Schwarzchild,
Reissner-Nordstrom and Kerr black holes. | gr-qc |
Sensitivity to a Frequency-Dependent Circular Polarization in an
Isotropic Stochastic Gravitational Wave Background: We calculate the sensitivity to a circular polarization of an isotropic
stochastic gravitational wave background (ISGWB) as a function of frequency for
ground- and space-based interferometers and observations of the cosmic
microwave background. The origin of a circularly polarized ISGWB may be due to
exotic primordial physics (i.e., parity violation in the early universe) and
may be strongly frequency dependent. We present calculations within a coherent
framework which clarifies the basic requirements for sensitivity to circular
polarization, in distinction from previous work which focused on each of these
techniques separately. We find that the addition of an interferometer with the
sensitivity of the Einstein Telescope in the southern hemisphere improves the
sensitivity of the ground-based network to circular polarization by about a
factor of two. The sensitivity curves presented in this paper make clear that
the wide range in frequencies of current and planned observations ($10^{-18}\
{\rm Hz} \lesssim f \lesssim 100\ {\rm Hz}$) will be critical to determining
the physics that underlies any positive detection of circular polarization in
the ISGWB. We also identify a desert in circular polarization sensitivity for
frequencies between $10^{-15}\ {\rm Hz} \lesssim f \lesssim 10^{-3}\ {\rm Hz}$,
given the inability for pulsar timing arrays and indirect-detection methods to
distinguish the gravitational wave polarization. | gr-qc |
On the Physical Properties of Spherically Symmetric Self-Similar
Solutions: In this paper, we are exploring some of the properties of the self-similar
solutions of the first kind. In particular, we shall discuss the kinematic
properties and also check the singularities of these solutions. We discuss
these properties both in co-moving and also in non co-moving (only in the
radial direction) coordinates. Some interesting features of these solutions
turn up. | gr-qc |
Strong deflection limit of black hole gravitational lensing with
arbitrary source distances: The gravitational field of supermassive black holes is able to strongly bend
light rays emitted by nearby sources. When the deflection angle exceeds $\pi$,
gravitational lensing can be analytically approximated by the so-called strong
deflection limit. In this paper we remove the conventional assumption of
sources very far from the black hole, considering the distance of the source as
an additional parameter in the lensing problem to be treated exactly. We find
expressions for critical curves, caustics and all lensing observables valid for
any position of the source up to the horizon. After analyzing the spherically
symmetric case we focus on the Kerr black hole, for which we present an
analytical 3-dimensional description of the higher order caustic tubes. | gr-qc |
On the viability of quintessential inflationary models from
observational data: Assuming that primordial density fluctuationas are nearly Gaussian, from a
frequentist viewpoint, the two-dimensional marginalized joint coincidence
contour in the plane $(n_s,r)$ (being $n_s$ the spectral index and $r$ the
ratio of tensor to scalar perturbations), without the presence of running is
usually used to test the viability of the inflationary models. The models that
provide, between $50$ and $60$ e-folds, a curve in that plane, which lies
outside the $95.5 \%$ C.L are ruled out. I will basically argue that the this
low number of e-folds is unjustified, and that models leading to a theoretical
value of the running different from zero must be checked with observational
data allowing the running. When both prescriptions are taken into account,
dealing in the context of quintessential inflation, i.e. when the potential is
a combination of an inflationary with a quintessential one that leads to a
deflationary regime, inflationary models such as the quartic or the Higgs
potential are allowed. | gr-qc |
The affine-null formulation of the gravitational equations: spherical
case: A new evolution algorithm for the characteristic initial value problem based
upon an affine parameter rather than the areal radial coordinate used in the
Bondi-Sachs formulation is applied in the spherically symmetric case to the
gravitational collapse of a massless scalar field. The advantages over the
Bondi-Sachs version are discussed, with particular emphasis on the application
to critical collapse. Unexpected quadratures lead to a simple evolution
algorithm based upon ordinary differential equations which can be integrated
along the null rays. For collapse to a black hole in a Penrose compactified
spacetime, these equations are regularized throughout the exterior and interior
of the horizon up to the final singularity. They are implemented as a global
numerical evolution code based upon the Galerkin method. New results regarding
the global properties of critical collapse are presented. | gr-qc |
Causal relation between regions I and IV of the Kruskal extension: By extending the exterior Schwarzschild spacetime in two opposite directions
with the Kruskal method, we get an extension which has the same T-X spacetime
diagram as has the conventional Kruskal extension, while allowing its regions I
and IV to correspond to different directions of the original spacetime. We
further extend the exterior Schwarzschild spacetime in all directions and get a
4-dimensional form of the Kruskal extension. The new form of extension includes
the conventional one as a part of itself. From the point of view of the
4-dimensional form, region IV of the conventional extension does not belong to
another universe but is a portion of the same exterior Schwarzschild spacetime
that contains region I. The two regions are causally related: particles can
move from one to the other. | gr-qc |
Classification theorem and properties of singular solutions to the
Tolman-Oppenheimer-Volkoff equation: The Tolman-Oppenheimer-Volkoff (TOV) equation admits singular solutions in
addition to regular ones. Here, we prove the following theorem. For any
equation of state that (i) is obtained from an entropy function, (ii) has
positive pressure and (iii) satisfies the dominant energy condition, the TOV
equation can be integrated from a boundary inwards to the center. Hence,
thermodynamic consistency of the EoS precludes pathological solutions, in which
the integration terminates at finite radius (because of horizons, or
divergences / zeroes of energy density). At the center, the mass function
either vanishes (regular solutions) or it is negative (singular solutions). For
singular solutions, the metric at the center is locally isomorphic to
negative-mass Schwarzschild spacetime. This means that matter is stabilized
because the singularity is strongly repulsive. We show that singular solutions
are causally well behaved: they are bounded-acceleration complete, and they are
conformal to a globally hyperbolic spacetime with boundary. Finally, we show
how to modify unphysical equations of state in order to obtain non-pathological
solutions, and we undertake a preliminary investigation of dynamical stability
for singular solutions. | gr-qc |
Tidal heating and torquing of the primary black hole in eccentric-orbit,
non-spinning extreme-mass-ratio inspirals to 22PN order: We calculate the high-order post-Newtonian (PN) expansion of the energy and
angular momentum fluxes onto the horizon of a nonspinning black hole primary in
eccentric-orbit extreme-mass-ratio inspirals. The first-order black hole
perturbation theory calculation uses \textsc{Mathematica} and makes an analytic
expansion of the Regge-Wheeler-Zerilli functions using the Mano-Suzuki-Takasugi
formalism. The horizon absorption, or tidal heating and torquing, is calculated
to 18PN relative to the leading horizon flux (i.e., 22PN order relative to the
leading quadrupole flux at infinity). Each PN term is a function of
eccentricity $e$ and is calculated as a series to $e^{10}$. A second expansion,
to 10PN horizon-relative order (or 14PN relative to the flux at infinity), is
computed deeper in eccentricity to $e^{20}$. A number of resummed closed-form
functions are found for the low PN terms in the series. Using a separate
Teukolsky perturbation code, numerical comparisons are made to test how
accurate the PN expansion is when extended to a close $p=10$ orbit. We find
that the horizon absorption expansion is not as convergent as a previously
computed infinity-side flux expansion. However, given that the horizon
absorption is suppressed by 4PN, useful results can be obtained even with an
orbit as tight as this for $e \le 1/2$. Combining the present results with our
earlier expansion of the fluxes to infinity makes the knowledge of the total
dissipation known to 19PN for eccentric-orbit nonspinning EMRIs. | gr-qc |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.