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Radiation from a uniformly accelerating harmonic oscillator: We consider a radiation from a uniformly accelerating harmonic oscillator
whose minimal coupling to the scalar field changes suddenly. The exact time
evolutions of the quantum operators are given in terms of a classical solution
of a forced harmonic oscillator. After the jumping of the coupling constant
there occurs a fast absorption of energy into the oscillator, and then a slow
emission follows. Here the absorbed energy is independent of the acceleration
and proportional to the log of a high momentum cutoff of the field. The emitted
energy depends on the acceleration and also proportional to the log of the
cutoff. Especially, if the coupling is comparable to the natural frequency of
the detector ($e^2/(4m) \sim \omega_0$) enormous energies are radiated away
from the oscillator. | gr-qc |
Lifshitz cosmology: quantum vacuum and Hubble tension: Dark energy is one of the greatest scientific mysteries of today. The idea
that dark energy originates from quantum vacuum fluctuations has circulated
since the late '60s, but theoretical estimations of vacuum energy have
disagreed with the measured value by many orders of magnitude, until recently.
Lifshitz theory applied to cosmology has produced the correct order of
magnitude for dark energy. Furthermore, the theory is based on well-established
and experimentally well-tested grounds in atomic, molecular and optical
physics. In this paper, we confront Lifshitz cosmology with astronomical data.
We find that the dark-energy dynamics predicted by the theory is able to
resolve the Hubble tension, the discrepancy between the observed and predicted
Hubble constant within the standard cosmological model. The theory is
consistent with supernovae data, Baryon Acoustic Oscillations and the Cosmic
Microwave Background. Our findings indicate that Lifshitz cosmology is a
serious candidate for explaining dark energy. | gr-qc |
A comment on "How the cosmological constant is hidden by Planck scale
curvature fluctuations'': A recent preprint by Wang and Unruh [arXiv:1911.06110] contains a number of
criticisms of my paper, "Hiding the cosmological constant" [Phys. Rev. Lett.
123 (2019) 131302, arXiv:1809.08277]. While Wang and Unruh suggest an
interesting alternative scenario and raise an important conceptual question,
most of their criticisms are incorrect, in part because of misunderstandings
about averaging and about the nature of the "foamy" spacetimes considered in my
paper. | gr-qc |
Perturbations in the relaxation mechanism for a large cosmological
constant: Recently, a mechanism for relaxing a large cosmological constant (CC) has
been proposed [arxiv:0902.2215], which permits solutions with low Hubble rates
at late times without fine-tuning. The setup is implemented in the LXCDM
framework, and we found a reasonable cosmological background evolution similar
to the LCDM model with a fine-tuned CC. In this work we analyse analytically
the perturbations in this relaxation model, and we show that their evolution is
also similar to the LCDM model, especially in the matter era. Some tracking
properties of the vacuum energy are discussed, too. | gr-qc |
Anatomy of the binary black hole recoil: A multipolar analysis: We present a multipolar analysis of the gravitational recoil computed in
recent numerical simulations of binary black hole (BH) coalescence, for both
unequal masses and non-zero, non-precessing spins. We show that multipole
moments up to and including l=4 are sufficient to accurately reproduce the
final recoil velocity (within ~2%) and that only a few dominant modes
contribute significantly to it (within ~5%). We describe how the relative
amplitudes, and more importantly, the relative phases, of these few modes
control the way in which the recoil builds up throughout the inspiral, merger,
and ringdown phases. We also find that the numerical results can be reproduced
by an ``effective Newtonian'' formula for the multipole moments obtained by
replacing the radial separation in the Newtonian formulae with an effective
radius computed from the numerical data. Beyond the merger, the numerical
results are reproduced by a superposition of three Kerr quasi-normal modes
(QNMs). Analytic formulae, obtained by expressing the multipole moments in
terms of the fundamental QNMs of a Kerr BH, are able to explain the onset and
amount of ``anti-kick'' for each of the simulations. Lastly, we apply this
multipolar analysis to help explain the remarkable difference between the
amplitudes of planar and non-planar kicks for equal-mass spinning black holes. | gr-qc |
A note on the wave equation on black hole spacetimes with small
non-decaying first order terms: We present an elementary physical space argument to establish local
integrated decay estimates for the perturbed wave equation $\Box_g \phi =
\epsilon \beta^a \partial_a \phi$ on the exterior of the Schwarzschild geometry
$(\mathcal{M},g)$. Here $\beta$ is a regular vectorfield on $\mathcal{M}$
decaying suitably in space but not necessarily in time. The proof is formulated
to cover also perturbations of the Regge--Wheeler equation. | gr-qc |
Cosmological production of fermions in a flat Friedman universe with
linearly growing scale factor: exactly solvable model: We consider an exactly solvable model for production of fermions in the
Friedman flat universe with a scale factor linearly growing with time. Exact
solution expressed through the special functions admit an analytical
calculation of the number density of created particles. We also discuss in
general the role of the phenomenon of the cosmological particle production in
the history of universe. | gr-qc |
Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium
Formulation: We present a new numerical method for the construction of quasiequilibrium
models of black hole-neutron star binaries. We solve the constraint equations
of general relativity, decomposed in the conformal thin-sandwich formalism,
together with the Euler equation for the neutron star matter. We take the
system to be stationary in a corotating frame and thereby assume the presence
of a helical Killing vector. We solve these coupled equations in the background
metric of a Kerr-Schild black hole, which accounts for the neutron star's black
hole companion. In this paper we adopt a polytropic equation of state for the
neutron star matter and assume large black hole--to--neutron star mass ratios.
These simplifications allow us to focus on the construction of quasiequilibrium
neutron star models in the presence of strong-field, black hole companions. We
summarize the results of several code tests, compare with Newtonian models, and
locate the onset of tidal disruption in a fully relativistic framework. | gr-qc |
Periastron precession for an extremal spherically symmetric dilaton
black hole: The purpose of this article is to obtain the periastron precession of a free
particle moving around an extremal spherically symmetric dilaton black hole. To
get the formulae for the periastron precession we use the phase-plane analysis
of the general relativistic equations of motion. | gr-qc |
The geometry of the Barbour-Bertotti theories II. The three body problem: We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for $N\neq 3$, are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there. | gr-qc |
Cosmology from an exponential dependence on the trace of the
energy-momentum tensor -- Numerical approach and cosmological tests: In this paper, we present the cosmological scenario obtained from $f(R,T)$
gravity by using an exponential dependence on the trace of the energy-momentum
tensor. With a numerical approach applied to the equations of motion, we show
several precise fits and the respective cosmological consequences. As a matter
of completeness, we also analyzed cosmological scenarios where this new version
of $f(R,T)$ is coupled with a real scalar field. In order to find analytical
cosmological parameters, we used a slow-roll approximation for the evolution of
the scalar field. This approximation allowed us to derived the Hubble and the
deceleration parameters whose time evolutions describe the actual phase of
accelerated expansion, and corroborate with our numerical investigations.
Therefore, the analytical parameters unveil the viability of this proposal for
$f(R,T)$ in the presence of an inflaton field. | gr-qc |
Stationary axisymmetric SU(2) Einstein-Yang-Mills fields with restricted
circularity conditions are Abelian: In this paper we prove that in a stationary axisymmetric SU(2)
Einstein-Yang-Mills theory the most reasonable circularity conditions that can
be considered for the Yang-Mills fields imply in fact that the field is of
embedded Abelian type, or else that the metric is not asymptotically flat. | gr-qc |
Kinetic Scalar Curvature Extended $f(R)$ Gravity: In this work we study a modified version of vacuum $f(R)$ gravity with a
kinetic term which consists of the first derivatives of the Ricci scalar. We
develop the general formalism of this kinetic Ricci modified $f(R)$ gravity and
we emphasize on cosmological applications for a spatially flat cosmological
background. By using the formalism of this theory, we investigate how it is
possible to realize various cosmological scenarios. Also we demonstrate that
this theoretical framework can be treated as a reconstruction method, in the
context of which it is possible to realize various exotic cosmologies for
ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor
counterpart theory of this kinetic Ricci modified $f(R)$ gravity, and we show
the mathematical equivalence of the two theories. | gr-qc |
Minimally modified gravity with an auxiliary constraint: a Hamiltonian
construction: Working directly with a general Hamiltonian for the spacetime metric with the
$3+1$ decomposition and keeping only the spatial covariance, we investigate the
possibility of reducing the number of degrees of freedom by introducing an
auxiliary constraint. The auxiliary constraint is considered as part of the
definition of the theory. Through a general Hamiltonian analysis, we find the
conditions for the Hamiltonian as well as for the auxiliary constraint, under
which the theory propagates two tensorial degrees of freedom only. The class of
theories satisfying these conditions can be viewed as a new construction for
the type-II minimally modified gravity theories, which propagate the same
degrees of freedom of but are not equivalent to general relativity in the
vacuum. We also illustrate our formalism by a concrete example, and derive the
dispersion relation for the gravitational waves, which can be constrained by
observations. | gr-qc |
Mach's Principle and a Variable Speed of Light: Ernst Mach (1838-1916) suggested that the origin of gravitational interaction
could depend on the presence of all masses in the universe. A corresponding
hypothesis of Sciama (1953) on the gravitational constant, c^2/G = \sum
m_i/r_i, is linked to Dicke's (1957) proposal of an electromagnetic origin of
gravitation, a precursor of scalar-tensor-theories. In this an equivalent
description in terms of a variable speed of light (VSL) is given, and the
agreement with the four classical tests of general relativity is shown.
Moreover, VSL opens the possibility to write the total energy of a particle as
E=mc^2; this necessarily leads to the proportionality of inertial and
gravitating mass, the equivalence principle. Furthermore, a formula for c
depending on the mass distribution is given that reproduces Newton's law of
gravitation. This mass distribution allows to calculate a slightly variable
term that corresponds to the `constant' G. The present proposal may also supply
an alternative explanation to the flatness problem and the horizon problem in
cosmology. | gr-qc |
Renormalization, averaging, conservation laws and AdS (in)stability: We continue our analytic investigations of non-linear spherically symmetric
perturbations around the anti-de Sitter background in gravity-scalar field
systems, and focus on conservation laws restricting the (perturbatively) slow
drift of energy between the different normal modes due to non-linearities. We
discover two conservation laws in addition to the energy conservation
previously discussed in relation to AdS instability. A similar set of three
conservation laws was previously noted for a self-interacting scalar field in a
non-dynamical AdS background, and we highlight the similarities of this system
to the fully dynamical case of gravitational instability. The nature of these
conservation laws is best understood through an appeal to averaging methods
which allow one to derive an effective Lagrangian or Hamiltonian description of
the slow energy transfer between the normal modes. The conservation laws in
question then follow from explicit symmetries of this averaged effective
theory. | gr-qc |
Measuring a cosmological distance-redshift relationship using only
gravitational wave observations of binary neutron star coalescences: Detection of gravitational waves from the inspiral phase of binary neutron
star coalescence will allow us to measure the effects of the tidal coupling in
such systems. These effects will be measurable using 3rd generation
gravitational wave detectors, e.g. the Einstein Telescope, which will be
capable of detecting inspiralling binary neutron star systems out to redshift
z=4. Tidal effects provide additional contributions to the phase evolution of
the gravitational wave signal that break a degeneracy between the system's mass
parameters and redshift and thereby allow the simultaneous measurement of both
the effective distance and the redshift for individual sources. Using the
population of O(10^3-10^7) detectable binary neutron star systems predicted for
the Einstein Telescope the luminosity distance--redshift relation can be probed
independently of the cosmological distance ladder and independently of
electromagnetic observations. We present the results of a Fisher information
analysis applied to waveforms assuming a subset of possible neutron star
equations of state. We conclude that for our range of representative neutron
star equations of state the redshift of such systems can be determined to an
accuracy of 8-40% for z<1 and 9-65% for 1<z<4. | gr-qc |
Comments on the Canonical Measure in Cosmology: In the mini-superspace approximation to cosmology, the canonical measure can
be used to compute probabilities when a cutoff is introduced in the phase space
to regularize the divergent measure. However, the region initially constrained
by a simple cutoff evolves non-trivially under the Hamiltonian flow. We
determine the deformation of the regularized phase space along the orbits when
a cutoff is introduced for the scale factor of the universe or for the Hubble
parameter. In the former case, we find that the cutoff for the scale factor
varies in the phase space and effectively decreases as one evolves backwards in
time. In the later case, we calculate the probability of slow-roll inflation in
a chaotic model with a massive scalar, which turns out to be cutoff dependent
but not exponentially suppressed. We also investigate the measure problem for
non-abelian gauge fields giving rise to inflation. | gr-qc |
The Kinetics Of Nonequilibrium Universe. I. The Condition Of Local
Thermodynamical Equilibrium: In terms of fundamental principles of quantum theory of interacting particles
and relativistic kinetic theory there was carried out an analysis of the main
principle of standard cosmological scenario - the initial existence of local
thermodynamical equilibrium. It has been shown, that condition of the existence
of local thermodynamical equilibrium in Universe is determined essentially by
means of function of total cross-section of particles' interaction from the
kinematic invariant and in case of scaling's recovery in range of superhigh
energies it is initially broken. | gr-qc |
Quantum amplitudes in black-hole evaporation: Spins 1 and 2: Quantum amplitudes for $s=1$ at Maxwell fields and for $s=2$ linearised
gravitational wave perturbations of a spherically symmetric Einstein/massless
scalar background, describing gravitational collapse to a black hole, are
treated by analogy with a previous treatment of $s=0$ scalar-field
perturbations of gravitational collapse at late times. In both the $s=1$ and
$s=2$ cases, we isolate suitable 'co-ordinate' variables which can be taken as
boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we
take the data on an initial pre-collapse surface $\Sigma_I$ to be exactly
spherically symmetric. The (large) Lorentzian proper-time interval between
$\Sigma_{I}, \Sigma_{F}$, measured at spatial infinity, is denoted by $T$. The
complexified classical boundary-value problem is expected to be well-posed,
provide that the time interval $T$ has been rotated into the complex:
$T\to{\mid}T{\mid}\exp(-i\theta)$, for $0<\theta\leq{\pi}/2$. We calculate the
second-variation classical Lorenztian action $S ^{(2)}_{\rm class}$. Following
Feynman, we recover the Lorentzian quantum amplitude by taking the limit as
$\theta\to 0_+$ of the semi-classical amplitude $\exp(iS^{(2)}_{\rm class})$.
The boundary data for $ s=1$ involve the Maxwell magnetic field; the data for
$s=2$ involve the magnetic part of the Weyl curvature tensor. The magnetic
boundary conditions are related to each other and to the natural $s={1 \over
2}$ boundary conditions by supersymmetry. | gr-qc |
Charged black holes in expanding Einstein-de Sitter universes: Inspired in a previous work by McClure and Dyer (Classical Quantum Gravity
23, 1971 (2006)), we analyze some solutions of the Einstein-Maxwell equations
which were originally written to describe charged black holes in cosmological
backgrounds. A detailed analysis of the electromagnetic sources for a
sufficiently general metric is performed, and then we focus on deriving the
electromagnetic four-current as well as the conserved electric charge of each
metric. The charged McVittie solution is revisited and a brief study of its
causal structure is performed, showing that it may represent a charged black
hole in an expanding universe, with the black hole horizon being formed at
infinite late times. Charged versions of solutions originally put forward by
Vaidya (Vd) and Sultana and Dyer (SD) are also analyzed. It is shown that the
charged Sultana-Dyer metric requires a global electric current, besides a
central (pointlike) electric charge. With the aim of comparing to the charged
McVittie metric, new charged solutions of Vd and SD type are considered. In
these cases, the original mass and charge parameters are replaced by particular
functions of the cosmological time. In the new generalized charged Vaidya
metric the black hole horizon never forms, whereas in the new generalized
Sultana-Dyer case both the Cauchy and the black hole horizons develop at
infinite late times. A charged version of the Thakurta metric is also studied
here. It is also a new solution. As in the charged Sultana-Dyer case, the
natural source of the electromagnetic field is a central electric charge with
an additional global electric current. The global structure is briefly studied
and it is verified that the corresponding spacetime may represent a charged
black hole in a cosmological background. All the solutions present initial
singularities as found in the McVittie metric. | gr-qc |
GUP-Corrected van der Waals Black Holes: In this paper, we study the generalized uncertainty principle (GUP) effects
for the van der Waals (vdW) black holes. In order to obtain the GUP-corrected
solution, we consider GUP-corrected black hole temperature. We also study the
thermodynamics and phase transition of GUP-corrected vdW black holes. We
compare the differences between thermodynamic properties of both modified and
orginal solutions. We show that P-V criticality is physically acceptable in the
presence of GUP-correction. | gr-qc |
Black hole fusion in the extreme mass ratio limit: We present a simple, general, and accurate construction of the event horizons
for the fusion of two neutral, rotating black holes with arbitrary orientation
and values of their spins, in the extreme mass ratio limit where one black hole
is much larger than the other. We compute several parameters that characterize
the fusion and investigate their dependence on the black hole spin and
orientation axis. We also exhibit and study the appearance of transient
toroidal topology of the horizon. An earlier conjecture about universal
critical exponents before and after an axisymmetric pinch is proven. | gr-qc |
Gravitational Lensing by Charged Accelerating Black Holes: Current astrophysical observations show that on large scale the Universe is
electrically neutral. However, locally this may be quite different. Black holes
enveloped by a plasma in the presence of a strong magnetic field may have
acquired a significant electric charge. We can also expect that some of these
charged black holes are moving. Consequently to describe them we need spacetime
metrics describing moving black holes. In general relativity such a solution is
given by the charged C-de Sitter-metric. In this article we will assume that it
can be used to describe moving charged black holes. We will investigate how to
observe the electric charge using gravitational lensing. First we will use
elliptic integrals and functions to solve the geodesic equations. Then we will
derive lens equation, travel time and redshift. We will discuss the impact of
the electric charge on these observables and potential limitations for its
observation. | gr-qc |
Cosmology in Delta-Gravity: We present a model of the gravitational field based on two symmetric tensors.
Gravity is affected by the new field, but outside matter the predictions of the
model coincide exactly with general relativity, so all classical tests are
satisfied. We find that massive particles do not follow a geodesic while
massless particles trajectories are null geodesics of an effective metric. We
study the Cosmological case, where we get an accelerated expansion of the
universe without dark energy. We also introduce the possibility to explain dark
matter with $\tilde{\delta}$ gravity. | gr-qc |
Rapid and reliable sky localization of gravitational wave sources: The first detection of gravitational waves by LIGO from the merger of two
compact objects has sparked new interest in detecting electromagnetic
counterparts to these violent events. For mergers involving neutron stars, it
is thought that prompt high-energy emission in gamma rays and x-rays will be
followed days to weeks later by an afterglow in visible light, infrared and
radio. Rapid sky localization using the data from a network of gravitational
wave detectors is essential to maximize the chances of making a joint
detection. Here I describe a new technique that is able to produce accurate,
fully Bayesian sky maps in seconds or less. The technique can be applied to
spin-precessing compact binaries, and can take into account detector
calibration and spectral estimation uncertainties. | gr-qc |
Cylindrically Symmetric Solution in Teleparallel Theory of Gravitation: The field equations of a special class of teleparallel theory of gravitation
and electromagnetic fields have been applied to tetrad space having cylindrical
symmetry with four unknown functions of radial coordinate $r$ and azimuth angle
$\theta$. The vacuum stress-energy momentum tensor with one assumption
concerning its specific form generates one non-trivial exact analytic solution.
This solution is characterized by a constant magnetic field parameter $B_0$. If
$B_0=0$ then, the solution will reduces to the flat spacetime. The energy
content is calculated using the superpotential given in the framework of
teleparallel geometry. The energy contained in a sphere is found to be
different from the pervious results. | gr-qc |
Constraints on metric-affine gravity black holes from the stellar motion
at the Galactic Center: We consider a static, spherically symmetric space-time with an electric field
arising from a quadratic metric-affine extension of General Relativity. Such a
space-time is free of singularities in the centre of the black holes, while at
large distances it quickly boils down to the usual Reissner-Nordstr\"om
solution. We probe this space-time metric, which is uniquely characterized by
two length scales, $r_q$ and $\ell$, using the astrometric and spectroscopic
measurements of the orbital motion of the S2 star around the Galactic Center.
Our analysis constrains $r_q$ to be below $2.7M$ for values $\ell<120 AU$,
strongly favouring a central object that resembles a Schwarzschild black hole. | gr-qc |
The case for black hole thermodynamics, Part I: phenomenological
thermodynamics: I give a fairly systematic and thorough presentation of the case for
regarding black holes as thermodynamic systems in the fullest sense, aimed at
students and non-specialists and not presuming advanced knowledge of quantum
gravity. I pay particular attention to (i) the availability in classical black
hole thermodynamics of a well-defined notion of adiabatic intervention; (ii)
the power of the membrane paradigm to make black hole thermodynamics precise
and to extend it to local-equilibrium contexts; (iii) the central role of
Hawking radiation in permitting black holes to be in thermal contact with one
another; (iv) the wide range of routes by which Hawking radiation can be
derived and its back-reaction on the black hole calculated; (v) the
interpretation of Hawking radiation close to the black hole as a
gravitationally bound thermal atmosphere. In an appendix I discuss recent
criticisms of black hole thermodynamics by Dougherty and Callender. This paper
confines its attention to the thermodynamics of black holes; a sequel will
consider their statistical mechanics. | gr-qc |
Dimensionless physics: Planck constant as an element of Minkowski metric: Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear
combinations of the fermionis fields,\cite{Diakonov2011} suggests that in
general relativity the metric may have dimension 2, i.e.
$[g_{\mu\nu}]=1/[L]^2$. Several other approaches to quantum gravity, including
the model of superplastic vacuum and $BF$-theories of gravity support this
suggesuion. The important consequence of such metric dimension is that all the
diffeomorphism invariant quantities are dimensionless for any dimension of
spacetime. These include the action $S$, interval $s$, cosmological constant
$\Lambda$, scalar curvature $R$, scalar field $\Phi$, etc. Here we are trying
to further exploit the Diakonov idea, and consider the dimension of the Planck
constant. The application of the Diakonov theory suggests that the Planck
constant $\hbar$ is the parameter of the Minkowski metric. The Minkowski
parameter $\hbar$ is invariant only under Lorentz transformations, and is not
diffeomorphism invariant. As a result the Planck constant $\hbar$ has nonzero
dimension -- the dimension of length [L]. Whether this Planck constant length
is related to the Planck length scale, is an open question. In principle there
can be different Minkowski vacua with their own values of the parameter
$\hbar$. Then in the thermal contact between the two vacua their temperatures
obey the analog of the Tolman law: $\hbar_1/T_1= \hbar_2/T_2$. | gr-qc |
Consistency between dynamical and thermodynamical stabilities for
perfect fluid in $f(R)$ theories: We investigate the stability criterions for perfect fluid in $f(R)$ theories
which is an important generalization of general relativity. Firstly, using
Wald's general variation principle, we recast Seifert's work and obtain the
dynamical stability criterion. Then using our generalized thermodynamical
criterion, we obtain the concrete expressions of the criterion. We show that
the dynamical stability criterion is exactly the same as the thermodynamical
stability criterion. This result suggests that there is an inherent connection
between the thermodynamics and gravity in $f(R)$ theories. It should be pointed
out that using the thermodynamical method to determine the stability for
perfect fluid is simpler and more directly than the dynamical method. | gr-qc |
The orientations of the binary black holes in GWTC-3: It is expected that the orbital planes of gravitational-wave (GW) sources are
isotropically distributed. However, both physical and technical factors, such
as alternate theories of gravity with birefringence, catalog contamination, and
search algorithm limitations, could result in inferring a non-isotropic
distribution. Showing that the inferred astrophysical distribution of the
orbital orientations is indeed isotropic can thus be used to rule out some
violations of general relativity, as a null test about the purity of the GW
catalog sample, and as a check that selection effects are being properly
accounted for. We augment the default mass/spins/redshift model used by the
LIGO-Virgo-KAGRA Collaboration in their most recent analysis to also measure
the astrophysical distribution of orbital orientations. We show that the 69
binary black holes in GWTC-3 are consistent with having random orbital
orientations. The inferred distribution is highly symmetric around $\pi/2$,
with skewness $\mathcal{S}_{\rm{post}}=0.01^{+0.17}_{-0.17}$. Meanwhile, the
median of the inferred distribution has a Jensen-Shannon divergence of
$1.4\times 10^{-4}$ bits when compared to the expected isotropic distribution. | gr-qc |
Testing Lambert$W$ equation of state with observational Hubble parameter
data: In this paper, we investigate the possibility that the Universe is driven by
a single dark fluid described by a Lambert $W$ equation of state parameter,
$w_{eff}$, which is essentially dependent on two parameters $\vartheta_{1}$ and
$\vartheta_{2}$ which need to be fixed from observations. We obtain the
constraints on these parameters using the latest 51 data points of $H(z)$
measurements, spanning the redshift range $0.07\leq z \leq 2.36$. The present
study shows that the Universe is indeed undergoing an accelerated expansion
phase following the decelerated one at the transition redshift,
$z_{t}=0.77\pm0.03$ ($1\sigma$) and is well consistent with the recent
observations. We also find that at low redshifts, $w_{eff}$ evolves only in the
quintessence regime ($-1<w_{eff}<-\frac{1}{3}$) within $1\sigma$ confidence
level. Its present value is found to be $-0.96\pm0.02$ ($1\sigma$). The fact
that the present value of $w_{eff}$ is very close to the Cosmological Constant
$\Lambda$ implies that our proposed equation of state parameter might serve as
a unification of dark matter and dark energy. Furthermore, we compare the
evolution of $H(z)$ for the model under consideration with that of the
$\Lambda$CDM model. Finally, we observe that for the best-fit case, the
differences between the two models are negligible at $z\sim 0.67$. | gr-qc |
Primordial Black Hole formation from overlapping cosmological
fluctuations: We consider the formation of primordial black holes (PBHs), during the
radiation-dominated Universe, generated from the collapse of super-horizon
curvature fluctuations that are overlapped with others on larger scales. Using
a set of different curvature profiles, we show that the threshold for PBH
formation (defined as the critical peak of the compaction function) can be
decreased by several percentages, thanks to the overlapping between two peaks
in the profile of the compaction function. In the opposite case, when the
fluctuations are sufficiently decoupled the threshold values behave as having
the fluctuations isolated (isolated peaks). We find that the analytical
estimates of arXiv:1907.13311 can be used accurately when applied to the
corresponding peak that is leading to the gravitational collapse. We also study
in detail the dynamics and estimate the final PBH mass for different initial
configurations, showing that the profile dependence has a significant effect on
that. | gr-qc |
xPert: Computer algebra for metric perturbation theory: We present the tensor computer algebra package xPert for fast construction
and manipulation of the equations of metric perturbation theory, around
arbitrary backgrounds. It is based on the combination of explicit combinatorial
formulas for the n-th order perturbation of curvature tensors and their gauge
changes, and the use of highly efficient techniques of index canonicalization,
provided by the underlying tensor system xAct, for Mathematica. We give
examples of use and show the efficiency of the system with timings plots: it is
possible to handle orders n=4 or n=5 within seconds, or reach n=10 with timings
below 1 hour. | gr-qc |
Free and constrained symplectic integrators for numerical general
relativity: We consider symplectic time integrators in numerical General Relativity and
discuss both free and constrained evolution schemes. For free evolution of
ADM-like equations we propose the use of the Stoermer-Verlet method, a standard
symplectic integrator which here is explicit in the computationally expensive
curvature terms. For the constrained evolution we give a formulation of the
evolution equations that enforces the momentum constraints in a holonomically
constrained Hamiltonian system and turns the Hamilton constraint function from
a weak to a strong invariant of the system. This formulation permits the use of
the constraint-preserving symplectic RATTLE integrator, a constrained version
of the Stoermer-Verlet method.
The behavior of the methods is illustrated on two effectively 1+1-dimensional
versions of Einstein's equations, that allow to investigate a perturbed
Minkowski problem and the Schwarzschild space-time. We compare symplectic and
non-symplectic integrators for free evolution, showing very different numerical
behavior for nearly-conserved quantities in the perturbed Minkowski problem.
Further we compare free and constrained evolution, demonstrating in our
examples that enforcing the momentum constraints can turn an unstable free
evolution into a stable constrained evolution. This is demonstrated in the
stabilization of a perturbed Minkowski problem with Dirac gauge, and in the
suppression of the propagation of boundary instabilities into the interior of
the domain in Schwarzschild space-time. | gr-qc |
Improved dynamics and gravitational collapse of tachyon field coupled
with a barotropic fluid: We consider a spherically symmetric gravitational collapse of a tachyon field
with an inverse square potential, which is coupled with a barotropic fluid. By
employing an holonomy correction imported from loop quantum cosmology, we
analyse the dynamics of the collapse within a semiclassical description. Using
a dynamical system approach, we find that the stable fixed points given by the
standard general relativistic setting turn into saddle points in the present
context. This provides a new dynamics in contrast to the black hole and naked
singularities solutions appearing in the classical model. Our results suggest
that classical singularities can be avoided by quantum gravity effects and are
replaced by a bounce. By a thorough numerical studies we show that, depending
on the barotropic parameter $\gamma$, there exists a class of solutions
corresponding to either a fluid or a tachyon dominated regimes. Furthermore,
for the case $\gamma \sim 1$, we find an interesting tracking behaviour between
the tachyon and the fluid leading to a dust-like collapse. In addition, we show
that, there exists a threshold scale which determines when an outward energy
flux emerges, as a non-singular black hole is forming, at the corresponding
collapse final stages. | gr-qc |
Variational Principles in Teleparallel Gravity Theories: We study the variational principle and derivation of the field equations for
different classes of teleparallel gravity theories, using both their
metric-affine and covariant tetrad formulations. These theories have in common
that in addition to the tetrad or metric, they employ a flat connection as
additional field variable, but differ by the presence of absence of torsion and
nonmetricity for this independent connection. Besides the different underlying
geometric formulation using a tetrad or metric as fundamental field variable,
one has different choices to introduce the conditions of vanishing curvature,
torsion and nonmetricity, either by imposing them a priori and correspondingly
restricting the variation of the action when the field equations are derived,
or by using Lagrange multipliers. Special care must be taken, since these
conditions form non-holonomic constraints. Here we show explicitly that all of
the aforementioned approaches are equivalent, and that the same set of field
equations is obtained, independently of the choice of the geometric formulation
and variation procedure. We further discuss consequences arising from the
diffeomorphism invariance of the gravitational action, and show how they
establish relations between the gravitational field equations. | gr-qc |
Black Ring and Kerr Ellipsoid - Solitonic Configurations in Modified
Finsler Gravity: We study an effective Einstein-Finsler theory on tangent Lorentz bundle
constructed as a "minimal" extension of general relativity. Black ring and Kerr
like ellipsoid exact solutions and soliton configurations are presented. In
this endeavor the relevant metric depends not only on four dimensional
spacetime coordinates and also on velocity type variables that can be
interpreted as additional coordinates in the space of "extra dimensions". | gr-qc |
Exact solutions of Maxwell equations in homogeneous spaces with the
group of motions $G_3(VIII)$: The problem of classification of exact solutions of Maxwell's vacuum
equations for admissible electromagnetic fields and homogeneous space-time with
the group of motions $G_3(VIII)$ according to the Bianchi classification is
considered. All non-equivalent solutions are found. The classification problem
for remaining groups of motions $G_3(N)$ has already been solved in the other
papers. That is why all non-equivalent solutions of empty Maxwell equations for
all homogeneous spaces with admissible electromagnetic fields are known now. | gr-qc |
Superradiation of Dirac particles in KN black hole: In this article, we process the approximate wave function of the Dirac
particle outside the horizon of the KN ds black hole to effective potential V,
and then derive V (including real and imaginary parts). We know that fermions
cannot produce superradiation, but we can prove that Dirac particles in the KN
black hole background can have a special solution through a certain operation,
forming a Cooper pair, thus producing superradiation.We deal with the real and
imaginary parts separately. When V (real part or imaginary part) has a maximum
value, there may be a potential barrier outside the field of view to have a
chance to produce superradiation. | gr-qc |
Dynamics of Quintessence in Generalized Uncertainty Principle: We investigate the quintessence scalar field model modified by the
Generalized Uncertainty Principle in the background of a spatially flat
homogeneous and isotropic universe. By performing a dynamical system analysis
we examine the nature of the critical points and their stability for two
potentials, one is the exponential potential and the other is a general
potential. In the case of an exponential potential, we find some new critical
points for this modified quintessence scenario that describe the de Sitter
universe, and these critical points do not appear in the standard quintessence
model with an exponential potential. This is one of the main results of this
work. Now for the general potential our analysis shows that the physical
properties of the critical points remain exactly the same as for the
exponential potential which means that within this modified quintessence
scenario all kind of potentials have same behaviour. This kind of result is
completely new in cosmology because with the change of the potential,
differences are usually expected in all respect. | gr-qc |
A Bayesian Approach to the Detection Problem in Gravitational Wave
Astronomy: The analysis of data from gravitational wave detectors can be divided into
three phases: search, characterization, and evaluation. The evaluation of the
detection - determining whether a candidate event is astrophysical in origin or
some artifact created by instrument noise - is a crucial step in the analysis.
The on-going analyses of data from ground based detectors employ a frequentist
approach to the detection problem. A detection statistic is chosen, for which
background levels and detection efficiencies are estimated from Monte Carlo
studies. This approach frames the detection problem in terms of an infinite
collection of trials, with the actual measurement corresponding to some
realization of this hypothetical set. Here we explore an alternative, Bayesian
approach to the detection problem, that considers prior information and the
actual data in hand. Our particular focus is on the computational techniques
used to implement the Bayesian analysis. We find that the Parallel Tempered
Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases
of the anaylsis in a coherent framework. The signals are found by locating the
posterior modes, the model parameters are characterized by mapping out the
joint posterior distribution, and finally, the model evidence is computed by
thermodynamic integration. As a demonstration, we consider the detection
problem of selecting between models describing the data as instrument noise, or
instrument noise plus the signal from a single compact galactic binary. The
evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found
to be in close agreement with those computed using a Reversible Jump Markov
Chain Monte Carlo algorithm. | gr-qc |
Dynamical system analysis for nonminimal torsion-matter coupled gravity: In this work, we perform a detailed dynamical analysis for the cosmological
applications of a nonminimal torsion-matter coupled gravity. Two alternative
formalisms are proposed, which enable one to choose between the easier approach
for a given problem, and furthermore, we analyze six specific models. In
general, we extract fixed points corresponding either to dark-matter dominated,
scaling decelerated solutions, or to dark-energy dominated accelerated
solutions. Additionally, we find that there is a small parameter region in
which the model can experience the transition from the matter epoch to a
dark-energy era. These features are in agreement with the observed universe
evolution, and make the theory a successful candidate for the description of
Nature. | gr-qc |
Radiant gravitational collapse with anisotropy in pressures and bulk
viscosity: We model a compact radiant star that undergoes gravitational collapse from a
certain initial static configuration until it becomes a black hole. The star
consists of a fluid with anisotropy in pressures, bulk viscosity, in addition
to the radial heat flow. A solution of Einstein's field equations with temporal
dependence was presented to study the dynamic evolution of physical quantities,
such as the mass-energy function, the luminosity seen by an observer at
infinity and the heat flow. We checked the acceptability conditions of the
initial static configuration to obtain a range of mass-to-radius ratio in which
the presented star model is physically reasonable. The energy conditions were
analyzed for the dynamic case, in order to guarantee that the model is composed
of a physically acceptable fluid within the range of the mass-to-radius ratio
obtained for the static configuration or if they will be modified during the
collapse | gr-qc |
A Kinematical Approach to Conformal Cosmology: We present an alternative cosmology based on conformal gravity, as originally
introduced by H. Weyl and recently revisited by P. Mannheim and D. Kazanas.
Unlike past similar attempts our approach is a purely kinematical application
of the conformal symmetry to the Universe, through a critical reanalysis of
fundamental astrophysical observations, such as the cosmological redshift and
others. As a result of this novel approach we obtain a closed-form expression
for the cosmic scale factor R(t) and a revised interpretation of the space-time
coordinates usually employed in cosmology. New fundamental cosmological
parameters are introduced and evaluated. This emerging new cosmology does not
seem to possess any of the controversial features of the current standard
model, such as the presence of dark matter, dark energy or of a cosmological
constant, the existence of the horizon problem or of an inflationary phase.
Comparing our results with current conformal cosmologies in the literature, we
note that our kinematic cosmology is equivalent to conformal gravity with a
cosmological constant at late (or early) cosmological times. The cosmic scale
factor and the evolution of the Universe are described in terms of several
dimensionless quantities, among which a new cosmological variable delta emerges
as a natural cosmic time. The mathematical connections between all these
quantities are described in details and a relationship is established with the
original kinematic cosmology by L. Infeld and A. Schild. The mathematical
foundations of our kinematical conformal cosmology will need to be checked
against current astrophysical experimental data, before this new model can
become a viable alternative to the standard theory. | gr-qc |
Neutral particle motion around a Schwarzschild-de Sitter Black Hole in
f(R) gravity: This article investigates the presence of a static spherically symmetric
solution in the metric f(R) gravity. Consequently, we have examined the
presence of horizons for the extreme and hyperextreme Schwarzschild-de Sitter
solution. Further, we have investigated the orbital motion of a time-like
particle around the Schwarzschild-dS solution by forming the constraints for
the existence of circular orbits and have subsequently developed an
approximation to the innermost stable circular orbit (ISCO). | gr-qc |
Collisions in piecewise flat gravity in 3+1 dimensions: We consider the (3+1)-dimensional locally finite gravity model proposed by 't
Hooft. In particular we revisit the problem of resolving collisions of string
defects. We provide a new geometric description of the configurations of
strings using piecewise flat manifolds, and use it to resolve a more general
class of collisions. We argue that beyond certain bounds for the
deficiency/surplus angles no resolutions may be found that satisfy the imposed
causality conditions. | gr-qc |
Lichnerowicz-Type Theorems for Self-gravitating Systems with Nonlinear
Electromagnetic Fields: We consider a self-gravitating system containing a globally timelike Killing
vector and a nonlinear Born-Infeld electromagnetic field and scalar fields. We
prove that under certain boundary conditions (asymptotically flat/AdS) there
can't be any nontrivial field configurations in the spacetime. To explore
nontrivial solutions one should break any of the conditions we imposed. The
case with another type of nonlinear electromagnetic field is also analyzed, and
similar conclusions have been obtained under certain conditions. | gr-qc |
On Poincaré gauge theory of gravity, its equations of motion, and
Gravity Probe B: Ever since E.Cartan in the 1920s enriched the geometric framework of general
relativity (GR) by introducing a {\it torsion} of spacetime, the question arose
whether one could find a measurement technique for detecting the presence of a
torsion field. Mao et al.(2007) claimed that the rotating quartz balls in the
gyroscopes of the Gravity Probe B experiment, falling freely on an orbit around
the Earth, should "feel" the torsion. Similarly, March et al.(2011) argue with
the precession of the Moon and the Mercury and extend later their
considerations to the Lageos satellite.--- A consistent theory of gravity with
torsion emerged during the early 1960's as gauge theory of the Poincar\'e
group. This Poincar\'e gauge theory of gravity incorporates as simplest viable
cases the Einstein-Cartan(-Sciama-Kibble) theory (EC), the teleparallel
equivalent GR|| of GR, and GR itself. So far, PG and, in particular, the
existence of torsion have {\it not} been experimentally confirmed. However, PG
is to be considered as the standard theory of gravity with torsion because of
its very convincing gauge structure.--- Since the early 1970s up to today,
different groups have shown more or less independently that torsion couples
only to the {\it elementary particle spin} and under no circumstances to the
orbital angular momentum of test particles. This is established knowledge and
we reconfirm this conclusion by discussing the energy-momentum law of PG, which
has same form for all versions of PG. Therefore, we conclude that,
unfortunately, the investigations of Mao et al. and March et al. do not yield
any information on torsion. | gr-qc |
Vistas in numerical relativity: Upcoming gravitational wave-experiments promise a window for discovering new
physics in astronomy. Detection sensitivity of the broadband laser
interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with
accurate wave-form templates. Where analytic methods break down, we have to
resort to numerical relativity, often in Hamiltonian or various hyperbolic
formulations. Well-posed numerical relativity requires consistency with the
elliptic constraints of energy and momentum conservation. We explore this using
a choice of gauge in the future and a dynamical gauge in the past. Applied to a
polarized Gowdy wave, this enables solving {\em all} ten vacuum Einstein
equations. Evolution of the Schwarzschild metric in 3+1 and, more generally,
sufficient conditions for well-posed numerical relativity continue to be open
challenges. | gr-qc |
Multi-scale analysis of the electromagnetic self-force in a weak
gravitational field: We examine the motion of a charged particle in a weak gravitational field. In
addition to the Newtonian gravity exerted by a large central body, the particle
is subjected to an electromagnetic self-force that contains both a conservative
piece and a radiation-reaction piece. This toy problem shares many of the
features of the strong-field gravitational self-force problem, and it is
sufficiently simple that it can be solved exactly with numerical methods, and
approximately with analytical methods. We submit the equations of motion to a
multi-scale analysis, and we examine the roles of the conservative and
radiation-reaction pieces of the self-force. We show that the
radiation-reaction force drives secular changes in the orbit's semilatus rectum
and eccentricity, while the conservative force drives a secular regression of
the periapsis and affects the orbital time function; neglect of the
conservative term can hence give rise to an important phasing error. We next
examine what might be required in the formulation of a reliable adiabatic
approximation for the orbital evolution; this would capture all secular changes
in the orbit and discard all irrelevant oscillations. We conclude that such an
approximation would be very difficult to formulate without prior knowledge of
the exact solution. | gr-qc |
Essentials of Classical Brane Dynamics: This article provides a self contained overview of the geometry and dynamics
of relativistic brane models, of the category that includes point particle,
string, and membrane representations for phenomena that can be considered as
being confined to a worldsheet of the corresponding dimension (respectively
one, two, and three) in a thin limit approximation in an ordinary 4 dimensional
spacetime background. This category also includes ``brane world'' models that
treat the observed universe as a 3-brane in 5 or higher dimensional background.
The first sections are concerned with purely kinematic aspects: it is shown
how, to second differential order, the geometry (and in particular the inner
and outer curvature) of a brane worldsheet of arbitrary dimension is
describable in terms of the first, second, and third fundamental tensor. The
later sections show how -- to lowest order in the thin limit -- the evolution
of such a brane worldsheet will always be governed by a simple tensorial
equation of motion whose left hand side is the contraction of the relevant
surface stress tensor $ bar T^{\mu\nu}$ with the (geometrically defined) second
fundamental tensor $K_{\mu\nu}{^\rho}$, while the right hand side will simply
vanish in the case of free motion and will otherwise be just the orthogonal
projection of any external force density that may happen to act on the brane. | gr-qc |
On the Development of the Concept of the Weak Cosmic Censorship
Conjecture in General Relativity: In this thesis, we scrutinize the literature to trace the evolution of the
concepts surrounding the weak cosmic censorship conjecture and the attempts to
prove or disprove it. We discuss its development over the years, its conceptual
transformations, and the various thought experiments constructed to validate or
invalidate the weak cosmic censorship conjecture. We also discuss possible
connections with blackhole thermodynamics, and end with an evaluation of the
current status about the subject, and finally, speculations about the future. | gr-qc |
Dirac fermions in de Sitter and anti-de Sitter backgrounds: Starting with a new theory of symmetries generated by isometries in field
theories with spin, one finds the generators of the spinor representation in
backgrounds with a given symmetry. In this manner one obtains a collection of
conserved operators from which one can chose the complete sets of commuting
operators defining quantum modes. In this framework, the quantum modes of the
free Dirac field on de Sitter or anti-de Sitter spacetimes can be completely
derived in static or moving charts. One presents the discrete quantum modes, in
the central static charts of the anti-de Sitter spacetime, whose eigenspinors
can be normalized. The consequence is that the second quantization can be done
in this case in canonical manner. For the free Dirac field on de Sitter
manifolds this can not be done in static charts being forced to consider the
moving ones. The quantum modes of the free Dirac field in these charts are used
for writing down the quantum Dirac field and its one-particle operators. | gr-qc |
Phase space of multi-fluid universe in $F(T)$-gravity and some
enhancements for the oscillating interaction model: Recently, a Friedmann-Robertson-Walker universe filled with various
cosmological fluids has been considered by S.D. Odintsov et al. in [30] from
phase space vantage point where various expressions for the Equation-of-State
(EoS) parameter were studied. Since these types of EoS parameters are
generative of appreciable results in the Hilbert-Einstein model, hence we
intend to investigate all the cases in a homogeneous $F(T)$-gravity ($T$ is the
torsion) through phase space analysis in precise detail. In short, three viable
models of interaction between dark matter and dark energy, including
usual-type, power-law type, and oscillating type, are investigated
comprehensively. It is indicated that the power-law interaction in the related
dynamical systems should be of increasing nature with time to get more critical
points. Due to the failure of the oscillating model of ref. [30] in
$F(T)$-gravity, four modified models are suggested and examined in both $F(T)$
and Hilbert-Einstein models. As to be seen, the modified models not only are
generative of critical points equivalent to that of ref. [30], but also give
rise to further critical points covering crucial stages of the evolution of the
universe. In the context of these four models, such as the old one, at early
times the interactions are negligible and they commence to grow as the cosmic
time approaches the late-time in which the unification of early inflation and
late acceleration is obtained. Using an indirect method, it is shown that the
oscillating models have substantial roles in transitions between eras. | gr-qc |
An extended solution space for Chern-Simons gravity: the slowly rotating
Kerr black hole: In the Einstein-Cartan formulation, an iterative procedure to find solutions
in non-dynamical Chern-Simons (CS) gravity in vacuum is proposed. The
iterations, in powers of a small parameter $\beta$ which codifies the CS
coupling, start from an arbitrary torsionless solution of Einstein equations.
With Schwarzschild as the zeroth-order choice, we derive a second-order
differential equation for the $\mathcal{O}(\beta)$ corrections to the metric,
for an arbitrary zeroth-order embedding parameter. In particular, the slowly
rotating Kerr metric is an $\mathcal{O}(\beta)$ solution in either the
canonical or the axial embeddings. | gr-qc |
Static Einstein-Maxwell black holes with no spatial isometries in AdS
space: We explicitly construct static black hole solutions to the fully non-linear,
D=4, Einstein-Maxwell-AdS equations that have no continuous spatial symmetries.
These black holes have a smooth, topologically spherical horizon (section), but
without isometries, and approach, asymptotically, global AdS spacetime. They
are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS
solitons recently discovered, for appropriate boundary data. In sharp contrast
with the uniqueness results for Minkowski electrovacuum, the existence of these
black holes shows that single, equilibrium, BH solutions in AdS-electrovacuum
admit an arbitrary multipole structure. | gr-qc |
Self-force: Computational Strategies: Building on substantial foundational progress in understanding the effect of
a small body's self-field on its own motion, the past 15 years has seen the
emergence of several strategies for explicitly computing self-field corrections
to the equations of motion of a small, point-like charge. These approaches
broadly fall into three categories: (i) mode-sum regularization, (ii) effective
source approaches and (iii) worldline convolution methods. This paper reviews
the various approaches and gives details of how each one is implemented in
practice, highlighting some of the key features in each case. | gr-qc |
Determination of new coefficients in the angular momentum and energy
fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio
inspirals using mode-by-mode fitting: We present an extension of work in an earlier paper showing high precision
comparisons between black hole perturbation theory and post-Newtonian (PN)
theory in their region of overlapping validity for bound, eccentric-orbit,
Schwarzschild extreme-mass-ratio inspirals. As before we apply a numerical
fitting scheme to extract eccentricity coefficients in the PN expansion of the
gravitational wave fluxes, which are then converted to exact analytic form
using an integer-relation algorithm. In this work, however, we fit to
individual $lmn$ modes to exploit simplifying factorizations that lie therein.
Since the previous paper focused solely on the energy flux, here we concentrate
initially on analyzing the angular momentum flux to infinity. A first step
involves finding convenient forms for hereditary contributions to the flux at
low-PN order, analogous to similar terms worked out previously for the energy
flux. We then apply the upgraded techniques to find new PN terms through 9PN
order and (at many PN orders) to $e^{30}$ in the power series in eccentricity.
With the new approach applied to angular momentum fluxes, we return to the
energy fluxes at infinity to extend those previous results. Like before, the
underlying method uses a \textsc{Mathematica} code based on use of the
Mano-Suzuki-Takasugi (MST) function expansion formalism to represent
gravitational perturbations and spectral source integration (SSI) to find
numerical results at arbitrarily high precision. | gr-qc |
Testing angular momentum effects on the space time: The paper contains a proposed experiment for testing the angular momentum
effect on the propagation of light around a rotating mass. The idea is to use a
rotating spherical laboratory-scale shell, around which two mutually orthogonal
light guides are wound acting as the arms of an interferometer. Numerical
estimates show that time of flight differences between the equatorial and polar
guides could be in the order of $\sim 10^{-20}$ s per loop. Using a few
thousands loops the time difference is brought in the range of feasible
interference measurements. | gr-qc |
5D black holes in Einstein-Gauss-Bonnet gravity with a background of
modified Chaplygin gas: Supposing the existence of modified Chaplygin gas with the equation of state
$p=A\rho-B/\rho^\beta$ as a cosmic background, we obtain a static
spherically-symmetric black hole solution to the Einstein-Gauss-Bonnet
gravitational equations in 5D spacetime. The spacetime structure of the
obtained black hole solution is analyzed, also the related black hole
properties are studied by calculating the thermodynamical quantities. During
this process, effects of the Gauss-Bonnet coupling constant and the modified
Chaplygin gas parameters on black hole solution, as well as on its
thermodynamical properties are discussed. At the end, we study the quantum
tunneling of scalar particles and the propagating of scalar waves within the
background of modified Chaplygin gas. The study shows that the system is stable
under scalar perturbations and the Hawking radiation could stop at some point,
leaving an extremal black hole as remnant for evaporation. | gr-qc |
Hybrid Geometrodynamics: A Hamiltonian description of classical gravity
coupled to quantum matter: We generalize the Hamiltonian picture of General Relativity coupled to
classical matter, known as geometrodynamics, to the case where such matter is
described by a Quantum Field Theory in Curved Spacetime, but gravity is still
described by a classical metric tensor field over a spatial hypersurface and
its associated momentum. Thus, in our approach there is no non-dynamic
background structure, apart from the manifold of events, and the gravitational
and quantum degrees of freedom have their dynamics inextricably coupled. Given
the Hamiltonian natureof the framework, we work with the generators of
hypersurface deformations over the manifold of quantum states. The construction
relies heavily on the differential geometry of a fibration of the set of
quantum states over the set of gravitational variables. An important feature of
this work is the use of Gaussian measures over the space of matter fields and
of Hida distributions to define a common superspace to all possible Hilbert
spaces with different measures, to properly characterize the Schrodinger wave
functional picture of QFT in curved spacetime. This allows us to relate states
within different Hilbert spaces in the case of vacuum states or measures that
depend on the gravitational degrees of freedom, as the ones associated to
Ashtekar's complex structure. This is achieved through the inclusion of a
quantum Hermitian connection for the fibration, which will have profound
physical implications. The most remarkable physical features of the
construction are norm conservation of the quantum state (even if the total
dynamics are non-unitary), the clear identification of the hybrid conserved
quantities and the description of a dynamical backreaction of quantum matter on
geometry and vice versa, which shall modify the physical properties the
gravitational field would have in the absence of backreaction. | gr-qc |
Dirac star with SU(2) Yang-Mills and Proca fields: We study spherically symmetric strongly gravitating configurations supported
by nonlinear spinor fields and non-Abelian SU(2) Yang-Mills/Proca magnetic
fields. Regular asymptotically flat solutions describing objects with positive
Arnowitt-Deser-Misner masses are obtained numerically. When the mass of the
spinor fields is much smaller than the Planck mass, we find approximate
solutions that can describe systems with total masses comparable to the
Chandrasekhar mass and with effective radii of the order of kilometers. For the
values of the system free parameters used here, we show that the SU(2) magnetic
field always gives a small contribution to the total energy density and mass of
the configurations under investigation. From the astrophysical point of view,
one can regard such objects as magnetized Dirac stars. | gr-qc |
Cosmologies in Horndeski's second-order vector-tensor theory: Horndeski derived a most general vector-tensor theory in which the vector
field respects the gauge symmetry and the resulting dynamical equations are of
second order. The action contains only one free parameter, $\lambda$, that
determines the strength of the non-minimal coupling between the gauge field and
gravity. We investigate the cosmological consequences of this action and
discuss observational constraints. For $\lambda<0$ we identify singularities
where the deceleration parameter diverges within a finite proper time. This
effectively rules out any sensible cosmological application of the theory for a
negative non-minimal coupling. We also find a range of parameter that gives a
viable cosmology and study the phenomenology for this case. Observational
constraints on the value of the coupling are rather weak since the interaction
is higher-order in space-time curvature. | gr-qc |
Rotation in vacuum and scalar background: are there alternatives to
Newman-Janis algorithm?: The Newman-Janis algorithm is the standard approach to rotation in general
relativity which, in vacuum, builds the Kerr metric from the Schwarzschild
spacetime. Recently, we have shown that the same algorithm applied to the
Papapetrou antiscalar spacetime produces a rotational metric devoid of horizons
and ergospheres. Though exact in the scalar sector, this metric, however,
satisfies the Einstein equations only asymptotically. We argue that this
discrepancy between geometric and matter parts (essential only inside
gravitational radius scale) is caused by the violation of the Hawking-Ellis
energy conditions for the scalar energy-momentum tensor. The axial potential
functions entering the metrics appear to be of the same form both in vacuum and
scalar background, and they also coincide with the linearized Yang-Mills field,
which might hint at their common non-gravitational origin. As an alternative to
the Kerr-type spacetimes produced by Newman-Janis algorithm we suggest the
exact solution obtained by local rotational coordinate transformation from the
Schwarzschild spacetime. Then, comparison with the Kerr-type metrics shows that
the Lense-Thirring phenomenon might be treated as a coordinate effect, similar
to the Coriolis force. | gr-qc |
Gauging away Physics: We consider the recent argument by Higuchi, Marolf and Morrison [1] that a
nonlocal gauge transformation can be used to eliminate the infrared divergence
of the graviton propagator, when evaluated in Bunch-Davies vacuum on the open
coordinate submanifold of de Sitter space in transverse-traceless-synchronous
gauge. Because the transformation is not local, the equal time commutator of
undifferentiated fields no longer vanishes. From explicit examination of the
Wightman function we demonstrate that the transformation adds anti-sources in
the far future which cancel the bad infrared behavior but also change the
propagator equation. The same problem exists in the localized version of the
recent argument. Adding such anti-sources does not seem to be legitimate and
could be used to eliminate the infrared divergence of the massless, minimally
coupled scalar. The addition of such anti-sources in flat space QED could be
effected by an almost identical gauge transformation, and would seem to
eliminate the well known infrared divergences which occur in loop corrections
to exclusive amplitudes. | gr-qc |
Cosmological electromagnetic hopfions: It is shown that any mathematical solution for null electromagnetic field
knots in flat spacetime is also a null field knotted solution for cosmological
electromagnetic fields that may be obtained by replacing the time $t\rightarrow
\tau=\int dt/a$, where $a=a(t)$ is the scale factor of the Universe described
by the Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmology, and by adequately
rewriting the (empty flat spacetimes) electromagnetic fields solutions in a
medium defined by the FLRW metric. We found that the dispersion (evolutoion) of
electromagnetic hopfions is faster on cosmological scenarios. We discuss the
implications of these results for different cosmological models. | gr-qc |
On the Birth of a Closed Hyperbolic Universe: We clarify and develop the results of a previous paper on the birth of a
closed universe of negative spatial curvature and multiply connected topology.
In particular we discuss the initial instanton and the second topology change
in more detail. This is followed by a short discussion of the results. | gr-qc |
Unveiling the merger structure of black hole binaries in generic planar
orbits: The precise modeling of binary black hole coalescences in generic planar
orbits is a crucial step to disentangle dynamical and isolated binary formation
channels through gravitational-wave observations. The merger regime of such
coalescences exhibits a significantly higher complexity compared to the
quasicircular case, and cannot be readily described through standard
parameterizations in terms of eccentricity and anomaly. In the spirit of the
Effective One Body formalism, we build on the study of the test-mass limit, and
show how gauge-invariant combinations of the binary energy and angular
momentum, such as a dynamical "impact parameter" at merger, overcome this
challenge. These variables reveal simple "quasi-universal" structures of the
pivotal merger parameters, allowing to build an accurate analytical
representation of generic (bounded and dynamically-bounded) orbital
configurations. We demonstrate the validity of these analytical relations using
255 numerical simulations of bounded noncircular binaries with nonspinning
progenitors from the RIT and SXS catalogs, together with a custom dataset of
dynamical captures generated using the Einstein Toolkit, and test-mass data in
bound orbits. Our modeling strategy lays the foundations of accurate and
complete waveform models for systems in arbitrary orbits, bolstering
observational explorations of dynamical formation scenarios and the discovery
of new classes of gravitational wave sources. | gr-qc |
Unit-lapse versions of the Kerr spacetime: The Kerr spacetime is perhaps the most astrophysically important of the
currently known exact solutions to the Einstein field equations. Whenever
spacetimes can be put in unit-lapse form it becomes possible to identify some
very straightforward timelike geodesics, (the "rain" geodesics), making the
physical interpretation of these spacetimes particularly clean and elegant. The
most well-known of these unit-lapse formulations is the Painleve-Gullstrand
form of the Schwarzschild spacetime, though there is also a Painleve-Gullstrand
form of the Lense-Thirring (slow rotation) spacetime. More radically there are
also two known unit-lapse forms of the Kerr spacetime -- the Doran and Natario
metrics -- though these are not precisely in Painleve-Gullstrand form. Herein
we shall seek to explicate the most general unit-lapse form of the Kerr
spacetime. While at one level this is "merely" a choice of coordinates, it is a
strategically and tactically useful choice of coordinates, thereby making the
technically challenging but astrophysically crucial Kerr spacetime somewhat
easier to deal with. | gr-qc |
On the Solutions of infinite systems of linear equations: New theorems about the existence of solution for a system of infinite linear
equations with a Vandermonde type matrix of coefficients are proved. Some
examples and applications of these results are shown. In particular, a kind of
these systems is solved and applied in the field of the General Relativity
Theory of Gravitation. The solution of the system is used to construct a
relevant physical representation of certain static and axisymmetric solution of
the Einstein vacuum equations. In addition, a newtonian representation of these
relativistic solutions is recovered. It is shown as well that there exists a
relation between this application and the classical Haussdorff moment problem. | gr-qc |
Reconstruction of $Λ$CDM Universe in $f(Q)$ Gravity: In this manuscript, we present a number of fascinating explicit
reconstructions for the $f(Q)$ gravity from the background of
Friedmann-La\^imatre-Robertson-Walker (FLRW) evolution history. We find the
more general functions of non-metricity scalar $Q$ that admit exact
$\Lambda$CDM expansion history. Adding extra degrees of freedom to the matter
sector is the only method to get the scale factor to behave in this manner for
more generic functions of $Q$. In addition, a cosmological reconstruction for
modified $f(Q)$ gravity is constructed in terms of e-folding. It is shown how
any FLRW cosmology can arise from a specific $f(Q)$ theory. We also reconstruct
the well-known cosmological evolution for the specific examples of $\Lambda$CDM
cosmology. | gr-qc |
Measurability of the tidal deformability by gravitational waves from
coalescing binary neutron stars: Combining new gravitational waveforms derived by long-term (14--16 orbits)
numerical-relativity simulations with waveforms by an effective-one-body (EOB)
formalism for coalescing binary neutron stars, we construct hybrid waveforms
and estimate the measurability for the dimensionless tidal deformability of the
neutron stars, $\Lambda$, by advanced gravitational-wave detectors. We focus on
the equal-mass case with the total mass $2.7M_\odot$. We find that for an event
at a hypothetical effective distance of $D_{\rm eff}=200$ Mpc, the
distinguishable difference in the dimensionless tidal deformability will be
$\approx 100$, 400, and 800 at 1-$\sigma$, 2-$\sigma$, and 3-$\sigma$ levels,
respectively, for advanced LIGO. If the true equation of state is stiff and the
typical neutron-star radius is $R \gtrsim 13 $ km, our analysis suggests that
the radius will be constrained within $\approx 1$ km at 2-$\sigma$ level for an
event at $D_{\rm eff}=200$ Mpc. On the other hand, if the true equation of
state is soft and the typical neutron-star radius is $R\lesssim 12$ km , it
will be difficult to narrow down the equation of state among many soft ones,
although it is still possible to discriminate the true one from stiff equations
of state with $R\gtrsim 13$ km. We also find that gravitational waves from
binary neutron stars will be distinguished from those from spinless binary
black holes at more than 2-$\sigma$ level for an event at $D_{\rm eff}=200$
Mpc. The validity of the EOB formalism, Taylor-T4, and Taylor-F2 approximants
as the inspiral waveform model is also examined. | gr-qc |
Coulomb and quantum oscillator problems in conical spaces with arbitrary
dimensions: The Schr\"odinger equations for the Coulomb and the Harmonic oscillator
potentials are solved in the cosmic-string conical space-time. The spherical
harmonics with angular deficit are introduced.
The algebraic construction of the harmonic oscillator eigenfunctions is
performed through the introduction of non-local ladder operators. By exploiting
the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues
for the angular momentum operators in three dimensions are reproduced.
A generalization for N-dimensions is performed for both Coulomb and harmonic
oscillator problems in angular deficit space-times.
It is thus established the connection among the states and energies of both
problems in these topologically non-trivial space-times. | gr-qc |
(3+1)-Formulation for Gravity with Torsion and Non-Metricity: The
Stress-Energy-Momentum Equation: We derive the generalized Gauss-Codazzi-Mainardi (GCM) equation for a general
affine connection with torsion and non-metricity. Moreover, we show that the
metric compatibility and torsionless condition of a connection on a manifold
are inherited to the connection of its hypersurface. As a physical application
to these results, we derive the (3+1)-Einstein Field Equation (EFE) for a
special case of Metric-Affine f(R)-gravity when f(R)=R, the Metric-Affine
General Relativity (MAGR). Motivated by the concept of geometrodynamics, we
introduce additional variables on the hypersurface as a consequence of
non-vanishing torsion and non-metricity. With these additional variables, we
show that for MAGR, the energy, momentum, and the stress-energy part of the EFE
are dynamical, i.e., all of them contain the derivative of a quantity with
respect to the time coordinate. For the Levi-Civita connection, one could
recover the Hamiltonian and the momentum (diffeomorphism) constraint, and
obtain the standard dynamics of GR. | gr-qc |
Geometrical Constraints on the Cosmological Constant: The cosmological constant problem is examined under the assumption that the
extrinsic curvature of the space-time contributes to the vacuum. A compensation
mechanism based on a variable cosmological term is proposed. Under a suitable
hypothesis on the behavior of the extrinsic curvature, we find that an
initially large $\Lambda(t)$ rolls down rapidly to zero during the early stages
of the universe. Using perturbation analysis, it is shown that such vacuum
behaves essentially as a spin-2 field which is independent of the metric. | gr-qc |
The quantization of a Kerr-AdS black hole: We apply our model of quantum gravity to a Kerr-AdS spacetime of dimension $2
m+1$, $m\ge2$, where all rotational parameters are equal, resulting in a wave
equation in a quantum spacetime which has a sequence of solutions that can be
expressed as a product of stationary and temporal eigenfunctions. The
stationary eigenfunctions can be interpreted as radiation and the temporal as
gravitational waves. The event horizon corresponds in the quantum model to a
Cauchy hypersurface that can be crossed by causal curves in both directions
such that the information paradox does not occur. We also prove that the
Kerr-AdS spacetime can be maximally extended by replacing in a generalized
Boyer-Lindquist coordinate system the $r$ variable by $\rho=r^2$ such that the
extended spacetime has a timelike curvature singularity in $\rho=-a^2$. | gr-qc |
Faster-than-c signals, special relativity, and causality: Motivated by the recent attention on superluminal phenomena, we investigate
the compatibility between faster-than-c propagation and the fundamental
principles of relativity and causality. We first argue that special relativity
can easily accommodate -- indeed, does not exclude -- faster-than-c signalling
at the kinematical level. As far as causality is concerned, it is impossible to
make statements of general validity, without specifying at least some features
of the tachyonic propagation. We thus focus on the Scharnhorst effect
(faster-than-c photon propagation in the Casimir vacuum), which is perhaps the
most plausible candidate for a physically sound realization of these phenomena.
We demonstrate that in this case the faster-than-c aspects are ``benign'' and
constrained in such a manner as to not automatically lead to causality
violations. | gr-qc |
Coincidence detection of broadband signals by networks of the planned
interferometric gravitational wave detectors: We describe how the six planned detectors (2 LIGOs, VIRGO, GEO, AIGO, TAMA)
can be used to perform coincidence experiments for the detection of broadband
signals from either coalescing compact binaries or burst sources. We make
comparisons of the achievable sensitivities of these detectors under different
optical configurations and find that a meaningful coincidence experiment for
the detection of coalescing binary signals can only be performed by a network
where the LIGOs and VIRGO are operated in power recycling mode and other medium
scale detectors are operated in dual recycling mode. For the model of burst
waveform considered by us (i.e. uniform power upto 2000Hz), we find that the
relative sensitivity of the power-recycled VIRGO is quite high as compared to
others with their present design parameters and thus coincidence experiment
performed by including VIRGO in the network would not be a meaningful one. We
also calculate optimized values for the time-delay window sizes for different
possible networks. The effect of filtering on the calculation of thresholds has
also been discussed. We set the thresholds for different detectors and find out
the volume of sky that can be covered by different possible networks and the
corresponding rate of detection of coalescing binaries in the beginning of the
next century. We note that a coincidence experiment of power-recycled LIGOs and
VIRGO and dual-recycled GEO and AIGO can increase the volume of the sky covered
by 3.2 times as compared with only the power-recycled LIGO detectors and by 1.7
times the sky covered by the power-recycled LIGO-VIRGO network. These values
are far less than the range that can be covered by only the LIGO-VIRGO network
with dual recycling operation at a later stage, but the accuracy in the
determination of direction, distance and other source parameters will be much | gr-qc |
Cosmological implications of the transition from the false vacuum to the
true vacuum state: We study the cosmology with the running dark energy. The parametrization of
dark energy with the respect to the redshift is derived from the first
principles of quantum mechanics. Energy density of dark energy is obtained from
the quantum process of transition from the false vacuum state to the true
vacuum state. This is the class of the extended interacting $\Lambda$CDM
models. We consider the energy density of dark energy parametrization
$\rho_\text{de}(t)$, which follows from the Breit-Wigner energy distribution
function which is used to model the quantum unstable systems. The idea that
properties of the process of the quantum mechanical decay of unstable states
can help to understand the properties of the observed universe was formulated
by Krauss and Dent and this idea was used in our considerations. In the
cosmological model with the mentioned parametrization there is an energy
transfer between the dark matter and dark energy. In such a evolutional
scenario the universe is starting from the false vacuum state and going to the
true vacuum state of the present day universe. We find that the intermediate
regime during the passage from false to true vacuum states takes place. The
intensity of the analyzed process is measured by a parameter $\alpha$. For the
small value of $\alpha$ ($0<\alpha <0.4$) this intermediate (quantum) regime is
characterized by an oscillatory behavior of the density of dark energy while
the for $\alpha > 0.4$ the density of the dark energy simply jumps down. In
both cases (independent from the parameter $\alpha$) the today value of density
of dark energy is reached at the value of $0.7$. We estimate the cosmological
parameters for this model with visible and dark matter. This model becomes in
good agreement with the astronomical data and is practically indistinguishable
from $\Lambda$CDM model. | gr-qc |
Resonant-plane locking and spin alignment in stellar-mass black-hole
binaries: a diagnostic of compact-binary formation: We study the influence of astrophysical formation scenarios on the
precessional dynamics of spinning black-hole binaries by the time they enter
the observational window of second- and third-generation gravitational-wave
detectors, such as Advanced LIGO/Virgo, LIGO-India, KAGRA and the Einstein
Telescope. Under the plausible assumption that tidal interactions are efficient
at aligning the spins of few-solar mass black-hole progenitors with the orbital
angular momentum, we find that black-hole spins should be expected to
preferentially lie in a plane when they become detectable by gravitational-wave
interferometers. This "resonant plane" is identified by the conditions
\Delta\Phi=0{\deg} or \Delta\Phi=+/-180{\deg}, where \Delta\Phi is the angle
between the components of the black-hole spins in the plane orthogonal to the
orbital angular momentum. If the angles \Delta \Phi can be accurately measured
for a large sample of gravitational-wave detections, their distribution will
constrain models of compact binary formation. In particular, it will tell us
whether tidal interactions are efficient and whether a mechanism such as mass
transfer, stellar winds, or supernovae can induce a mass-ratio reversal (so
that the heavier black hole is produced by the initially lighter stellar
progenitor). Therefore our model offers a concrete observational link between
gravitational-wave measurements and astrophysics. We also hope that it will
stimulate further studies of precessional dynamics, gravitational-wave template
placement and parameter estimation for binaries locked in the resonant plane. | gr-qc |
Aspects of nonrelativistic quantum gravity: A nonrelativistic approach to quantum gravity is studied. At least for weak
gravitational fields it should be a valid approximation. Such an approach can
be used to point out problems and prospects inherent in a more exact theory of
quantum gravity, yet to be discovered. Nonrelativistic quantum gravity, e.g.,
shows promise for prohibiting black holes altogether (which would eliminate
singularities and also solve the black hole information paradox), gives
gravitational radiation even in the spherically symmetric case, and supports
non-locality (quantum entanglement). Its predictions should also be testable at
length scales well above the "Planck scale", by high-precision experiments
feasible with existing technology. | gr-qc |
Role of $σR^{2}+γR_{μν}T^{μν}$ Model on Anisotropic
Polytropes: This paper analyzes the anisotropic stellar evolution governed by a
polytropic equation of state in the framework of $f(R,T,Q)$ gravity, where
$Q=R_{ab}T^{ab}$. We construct the field equations, hydrostatic equilibrium
equation and trace equation to obtain their solutions numerically under the
influence of $\sigma R^{2}+\gamma Q$ gravity model, where $\sigma$ and $\gamma$
are arbitrary constants. We examine the dependence of various physical
characteristics such as radial/tangential pressure, energy density, anisotropic
factor, total mass and surface redshift for specific values of the model
parameters. The physical acceptability of the considered model is discussed by
verifying the validity of energy conditions, causality condition, and adiabatic
index. We also study the effects arising due to the strong non-minimal
matter-curvature coupling on anisotropic polytropes. It is found that the
polytropic stars are stable and their maximum mass point lies within the
required observational Chandrasekhar limit. | gr-qc |
Phantom thick brane in 5D bulk: A model of a thick brane in 5D bulk supported by two phantom scalar fields is
considered. The comparison with a thick brane supported by two usual scalar
fields is carried out. The distinctions between a thick brane supported by one
usual scalar field and our model have been pointed out. | gr-qc |
Screening the fifth force in the Horndeski's most general scalar-tensor
theories: We study how the Vainshtein mechanism operates in the most general
scalar-tensor theories with second-order equations of motion. The field
equations of motion, which can be also applicable to most of other screening
scenarios proposed in literature, are generally derived in a spherically
symmetric space-time with a matter source. In the presence of a field coupling
to the Ricci scalar, we clarify conditions under which the Vainshtein mechanism
is at work in a weak gravitational background. We also obtain the solutions of
the field equation inside a spherically symmetric body and show how they can be
connected to exterior solutions that accommodate the Vainshtein mechanism. We
apply our general results to a number of concrete models such as the
covariant/extended Galileons and the DBI Galileons with Gauss-Bonnet and other
terms. In these models the fifth force can be suppressed to be compatible with
solar-system constraints, provided that non-linear field kinetic terms coupled
to the Einstein tensor do not dominate over other non-linear field
self-interactions. | gr-qc |
Gravitational Waves detection and spectroscopy with a Double-slit
Quantum Eraser: We propose the use of heralded photons to detect Gravitational Waves (GWs).
Heralded photons are those photons that, produced during a parametric
downconversion process, are "labelled" by the detection and counting of
coincidences of their correlated or entangled twins and therefore can be
discriminated from the background noise, independently of the type of
correlation/entanglement used in the setup. Without losing any generality, we
illustrate our proposal with a gedankenexperiment, in which the presence of a
gravitational wave causes a relative rotation of the reference frames
associated to the double-slit and the test polarizer, respectively, of a
Walborn's quantum eraser \cite{wal02}. In this thought experiment, the GW is
revealed by the detection of heralded photons in the dark fringes of the
recovered interference pattern by the quantum eraser. Other types of
entanglement, such as momentum-space or energy-time, could be used to obtain
heralded photons to be used in the future with high-frequency GW
interferometric detectors when enough bright sources of correlated photons will
be available. | gr-qc |
Gravitational collapse and formation of a black hole in a type II
minimally modified gravity theory: We study the spherically symmetric collapse of a cloud of dust in VCDM, a
class of gravitational theories with two local physical degrees of freedom. We
find that the collapse corresponds to a particular foliation of the
Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a
constant trace for the extrinsic curvature relative to the time $t$ constant
foliation. For this solution, we find that the final state of the collapse
leads to a static configuration with the lapse function vanishing at a radius
inside the apparent horizon. Such a point is reached in an infinite time-$t$
interval, $t$ being the cosmological time, i.e. the time of an observer located
far away from the collapsing cloud. The presence of this vanishing lapse
endpoint implies the necessity of a UV completion to describe the physics
inside the resulting black hole. On the other hand, since the corresponding
cosmic time $t$ is infinite, VCDM can safely describe the whole history of the
universe at large scales without knowledge of the unknown UV completion,
despite the presence of the so-called shadowy mode. | gr-qc |
New variables for the Lemaître-Tolman-Bondi dust solutions: We re-examine the Lem\^aitre-Tolman-Bondi (LTB) solutions with a dust source
admitting symmetry centers. We consider as free parameters of the solutions the
initial value functions: $Y_i$, $\rho_i$ and $\Ri$, obtained by restricting the
curvature radius, $Y\equiv \sqrt{g_{\theta\theta}}$, the rest mass density,
$\rho$, and the 3-dimensional Ricci scalar of the rest frames, $\R$, to an
arbitrary regular Cauchy hypersurface, $\Ti$, marked by constant cosmic time
($t=t_i$). Using $Y_i$ to fix the radial coordinate and the topology
(homeomorphic class) of $\Ti$, and scaling the time evolution in terms of an
adimensional scale factor $y=Y/Y_i$, we show that the dynamics, regularity
conditions and geometric features of the models are determined by $\rho_i$,
$\Ri$ and by suitably constructed volume averages and contrast functions
expressible in terms of invariant scalars defined in $\Ti$. These quantities
lead to a straightforward characterization of initial conditions in terms of
the nature of the inhomogeneity of $\Ti$, as density and/or curvature
overdensities (``lumps'') and underdensities (''voids'') around a symmetry
center. In general, only models with initial density and curvature lumps evolve
without shell crossing singularities, though special classes of initial
conditions, associated with a simmultaneous big bang, allow for a regular
evolution for initial density and curvature voids. Specific restrictions are
found so that a regular evolution for $t>t_i$ is possible for initial voids. A
step-by-step guideline is provided for using the new variables in the
construction of LTB models and for plotting all relevant quantities. | gr-qc |
A universal threshold for primordial black hole formation: In this letter, we argue and show numerically that the threshold to form
primordial black holes from an initial spherically symmetric perturbation is,
to an excellent approximation, universal, whenever given in terms of the
compaction function averaged over a sphere of radius $r_m$, where $r_m$ is the
scale on which the compaction function is maximum. This can be understood as
the requirement that, for a black hole to form, each shell of the averaged
compaction function should have an amplitude exceeding the so-called
Harada-Yoo-Kohri limit. For a radiation dominated universe we argued, supported
by the numerical simulations, that this limit is $\delta_c = 0.40$, which is
slightly below the one quoted in the literature. Additionally, we show that the
profile dependence of the threshold for the compaction function is only
sensitive to its curvature at the maximum. We use these results to provide an
analytic formula for the threshold amplitude of the compaction function at its
maximum in terms of the normalised compaction function curvature at $r_m$. | gr-qc |
The imposition of Cauchy data to the Teukolsky equation III: The
rotating case: We solve the problem of expressing the Weyl scalars $\psi $ that describe
gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do
so we use geometrical identities (like the Gauss-Codazzi relations) as well as
Einstein equations. We are able to explicitly express $\psi $ and $\partial
_t\psi $ as functions only of the extrinsic curvature and the three-metric (and
geometrical objects built out of it) of a generic spacelike slice of the
spacetime. These results provide the link between initial data and $\psi $ to
be evolved by the Teukolsky equation, and can be used to compute the
gravitational radiation generated by two orbiting black holes in the close
limit approximation. They can also be used to extract waveforms from spacetimes
completely generated by numerical methods. | gr-qc |
Coherent states for quantum gravity: towards collective variables: We investigate the construction of coherent states for quantum theories of
connections based on graphs embedded in a spatial manifold, as in loop quantum
gravity. We discuss the many subtleties of the construction, mainly related to
the diffeomorphism invariance of the theory. Aiming at approximating a
continuum geometry in terms of discrete, graph-based data, we focus on coherent
states for collective observables characterizing both the intrinsic and
extrinsic geometry of the hypersurface, and we argue that one needs to revise
accordingly the more local definitions of coherent states considered in the
literature so far. In order to clarify the concepts introduced, we work through
a concrete example that we hope will be useful to applying coherent state
techniques to cosmology. | gr-qc |
Energy distribution of a regular black hole solution in
Einstein-nonlinear electrodynamics: In this work a study about the energy-momentum of a new four-dimensional
spherically symmetric, static and charged, regular black hole solution
developed in the context of general relativity coupled to nonlinear
electrodynamics is presented. Asymptotically, this new black hole solution
behaves as the Reissner-Nordstr\"om solution only for the particular value
{\mu}=4, where {\mu} is a positive integer parameter appearing in the mass
function of the solution. The calculations are performed by use of the
Einstein, Landau-Lifshitz, Weinberg and M{\o}ller energy-momentum complexes. In
all the aforesaid prescriptions, the expressions for the energy of the
gravitating system considered depend on the mass M of the black hole, its
charge q, a positive integer {\alpha} and the radial coordinate r. In all these
pseudotensorial prescriptions the momenta are found to vanish, while the
Landau-Lifshitz and Weinberg prescriptions give the same result for the energy
distribution. In addition, the limiting behavior of the energy for the cases r
tends toward infinity, r=0 and q=0 is studied. The special case {\mu}=4 and
{\alpha}=3 is also examined. We conclude that the Einstein and M{\o}ller
energy-momentum complexes can be considered as the most reliable tools for the
study of the energy-momentum localization of a gravitating system. | gr-qc |
Tails for the Einstein-Yang-Mills system: We study numerically the late-time behaviour of the coupled Einstein
Yang-Mills system. We restrict ourselves to spherical symmetry and employ
Bondi-like coordinates with radial compactification. Numerical results exhibit
tails with exponents close to -4 at timelike infinity $i^+$ and -2 at future
null infinity \Scri. | gr-qc |
Dynamical $F(R)$ gravities: It is offered that $F(R)-$modified gravities can be considered as
nonperturbative quantum effects arising from Einstein gravity. It is assumed
that nonperturbative quantum effects gives rise to the fact that the connection
becomes incompatible with the metric, the metric factors and the square of the
connection in Einstein - Hilbert Lagrangian have nonperturbative additions. In
the simplest approximation both additions can be considered as functions of one
scalar field. The scalar field can be excluded from the Lagrangian obtaining
$F(R)-$gravity. The essence of quantum correction to the affine connection as a
torsion is discussed. | gr-qc |
An Extension of the Quantum Theory of Cosmological Perturbations to the
Planck Era: Cosmological perturbations are generally described by quantum fields on
(curved but) classical space-times. While this strategy has a large domain of
validity, it can not be justified in the quantum gravity era where curvature
and matter densities are of Planck scale. Using techniques from loop quantum
gravity, the standard theory of cosmological perturbations is extended to
overcome this limitation. The new framework sharpens conceptual issues by
distinguishing between the true and apparent trans-Planckian difficulties and
provides sufficient conditions under which the true difficulties can be
overcome within a quantum gravity theory. In a companion paper, this framework
is applied to the standard inflationary model, with interesting implications to
theory as well as observations. | gr-qc |
Critical Collapse of an Ultrarelativistic Fluid in the $Γ\to 1$
Limit: In this paper we investigate the critical collapse of an ultrarelativistic
perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of
$\Gamma\to 1$. We calculate the limiting continuously self similar (CSS)
solution and the limiting scaling exponent by exploiting self-similarity of the
solution. We also solve the complete set of equations governing the
gravitational collapse numerically for $(\Gamma-1) = 10^{-2},...,10^{-6}$ and
compare them with the CSS solutions. We also investigate the supercritical
regime and discuss the hypothesis of naked singularity formation in a generic
gravitational collapse. The numerical calculations make use of advanced methods
such as high resolution shock capturing evolution scheme for the matter
evolution, adaptive mesh refinement, and quadruple precision arithmetic. The
treatment of vacuum is also non standard. We were able to tune the critical
parameter up to 30 significant digits and to calculate the scaling exponents
accurately. The numerical results agree very well with those calculated using
the CSS ansatz. The analysis of the collapse in the supercritical regime
supports the hypothesis of the existence of naked singularities formed during a
generic gravitational collapse. | gr-qc |
Non - Topological Solitons in a Non-minimally Coupled Scalar Field
Induced Gravity Theory: Properties of soliton stars that could be expected to naturally arise out of
a first order phase transition in non-minimally coupled scalar-field-induced
gravity theories are investigated. Of particular interest are configurations,
similar to Lee-Wick stars, with vanishing effective gravitational constant in
the interiors. | gr-qc |
Friedmann equations and cosmic bounce in a modified cosmological
scenario: In this work we present a derivation of modified Raychaudhuri and Friedmann
equations from a phenomenological model of quantum gravity based on the
thermodynamics of spacetime. Starting from general gravitational equations of
motion which encode low-energy quantum gravity effects, we found its particular
solution for homogenous and isotropic universes with standard matter content,
obtaining a modified Raychaudhuri equation. Then, we imposed local energy
conservation and used a perturbative treatment to derive a modified Friedmann
equation. The modified evolution in the early universe we obtained suggests a
replacement of the Big Bang singularity by a regular bounce. Lastly, we also
briefly discuss the range of validity of the perturbative approach and its
results. | gr-qc |
A phase space analysis for nonlinear bulk viscous cosmology: We consider a Friedmann-Robertson-Walker spacetime filled with both viscous
radiation and nonviscous dust. The former has a bulk viscosity which is
proportional to an arbitrary power of the energy density, i.e. $\zeta \propto
\rho_v^{\nu}$, and viscous pressure satisfying a nonlinear evolution equation.
The analysis is carried out in the context of dynamical systems and the
properties of solutions corresponding to the fixed points are discussed. For
some ranges of the relevant parameter $\nu$ we find that the trajectories in
the phase space evolve from a FRW singularity towards an asymptotic de Sitter
attractor, confirming and extending previous analysis in the literature. For
other values of the parameter, instead, the behaviour differs from previous
works. | gr-qc |
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