text
stringlengths 73
2.82k
| category
stringclasses 21
values |
|---|---|
Quantum Yang--Mills Dark Energy: In this short review, I discuss basic qualitative characteristics of quantum
non-Abelian gauge dynamics in the non-stationary background of the expanding
Universe in the framework of the standard Einstein--Yang--Mills formulation. A
brief outlook of existing studies of cosmological Yang--Mills fields and their
properties will be given. Quantum effects have a profound impact on the gauge
field-driven cosmological evolution. In particular, a dynamical formation of
the spatially-homogeneous and isotropic gauge field condensate may be
responsible for both early and late-time acceleration, as well as for dynamical
compensation of non-perturbative quantum vacua contributions to the ground
state of the Universe. The main properties of such a condensate in the
effective QCD theory at the flat Friedmann--Lema\'itre--Robertson--Walker
(FLRW) background will be discussed within and beyond perturbation theory.
Finally, a phenomenologically consistent dark energy can be induced dynamically
as a remnant of the QCD vacua compensation arising from leading-order
graviton-mediated corrections to the QCD ground state. | gr-qc |
Gravitons as Goldstone Modes and the Spontaneous Symmetry Breaking of
Diffeomorphism Invariance: We complement investigations of the gauge structure of general relativity
with an analysis of the physical consequences of the spontaneous breaking of
diffeomorphism invariance which manifests itself in e.g. the socalled Einstein
hole problem. We analyze the nature of the gravitons as Goldstone excitations
both in the classical and the quantum case. We show that the metrical field and
the classical space-time manifold play the role of an order parameter field and
order parameter manifold as macroscopic super structures living in an
underlying presumed quantum space-time. We furthermore relate our observations
to possible phase transitions in some pre big-bang era. | gr-qc |
Space-time as strongly bent plate: Futher development is made of a consept of space-time as multidimensional
elastic plate, proposed earlier in [20,21]. General equilibrium equations,
including 4-dimensional tangent stress tensor - energy-momentum tensor of
matter - are derived. Comparative analysis of multidimensional elasticity
theory (MET) and GR is given. Variational principle, boundary conditions,
energy-momentum tensor, matter and space-time signature are reviewed within the
context of MET. | gr-qc |
Generalized $f(R,φ,X)$ gravity and the late-time cosmic acceleration: High-precision observational data have confirmed with startling evidence that
the Universe is currently undergoing a phase of accelerated expansion. This
phase, one of the most important and challenging current problems in cosmology,
represents a new imbalance in the governing gravitational equations.
Historically, physics has addressed such imbalances by either identifying
sources that were previously unaccounted for, or by altering the gravitational
theory. Several candidates, responsible for this expansion, have been proposed
in the literature, in particular, dark energy models and modified gravity
models, amongst others. Outstanding questions are related to the nature of this
so-called "dark energy" that is driving this acceleration, and whether it is
due to the vacuum energy or a dynamical field. On the other hand, the late-time
cosmic acceleration may be due to modifications of General Relativity. In this
work we explore a generalised modified gravity theory, namely $f(R,\phi,X)$
gravity, where $R$ is the Ricci scalar, $\phi$ is a scalar field, and $X$ is a
kinetic term. This theory contains a wide range of dark energy and modified
gravity models. We considered specific models and applications to the late-time
cosmic acceleration. | gr-qc |
On obtaining classical mechanics from quantum mechanics: Constructing a classical mechanical system associated with a given quantum
mechanical one, entails construction of a classical phase space and a
corresponding Hamiltonian function from the available quantum structures and a
notion of coarser observations. The Hilbert space of any quantum mechanical
system naturally has the structure of an infinite dimensional symplectic
manifold (`quantum phase space'). There is also a systematic, quotienting
procedure which imparts a bundle structure to the quantum phase space and
extracts a classical phase space as the base space. This works straight
forwardly when the Hilbert space carries weakly continuous representation of
the Heisenberg group and recovers the linear classical phase space
$\mathbb{R}^{\mathrm{2N}}$. We report on how the procedure also allows
extraction of non-linear classical phase spaces and illustrate it for Hilbert
spaces being finite dimensional (spin-j systems), infinite dimensional but
separable (particle on a circle) and infinite dimensional but non-separable
(Polymer quantization). To construct a corresponding classical dynamics, one
needs to choose a suitable section and identify an effective Hamiltonian. The
effective dynamics mirrors the quantum dynamics provided the section satisfies
conditions of semiclassicality and tangentiality. | gr-qc |
Nonthermal nature of extremal Kerr black holes: Liberati, Rothman and Sonego have recently showed that objects collapsing
into extremal Reissner-Nordstrom black holes do not behave as thermal objects
at any time in their history. In particular, a temperature, and hence
thermodynamic entropy, are undefined for them. I demonstrate that the analysis
goes through essentially unchanged for Kerr black holes. | gr-qc |
Euclidean Maxwell-Einstein Theory: After reviewing the context in which Euclidean propagation is useful we
compare and contrast Euclidean and Lorentzian Maxwell-Einstein theory and give
some examples of Euclidean solutions. | gr-qc |
Beyond the Standard Model Explanations of GW190521: The LIGO/Virgo collaboration has recently announced the detection of a heavy
binary black hole merger, with component masses that cannot be explained by
standard stellar structure theory. In this letter we propose several
explanations based on models of new physics, including new light particle
losses, modified gravity, large extra dimensions, and a small magnetic moment
of the neutrino. Each of these affect the physics of the pair-instability
differently, leading to novel mechanisms for forming black holes inside the
black hole mass gap. | gr-qc |
Statefinders and observational measurement of superenergy: The superenergy of the universe is a tensorial quantity and it is a general
relativistic analogue of the Appell's energy of acceleration in classical
mechanics. We propose the measurement of this quantity by the observational
parameters such as the Hubble parameter, the deceleration parameter, the jerk
and the snap (kerk) known as statefinders. We show that the superenergy of
gravity requires only the Hubble and deceleration parameter to be measured,
while the superenergy of matter requires also the measurement of the
higher-order characteristics of expansion: the jerk and the snap. In such a
way, the superenergy becomes another parameter characterizing the evolution of
the universe. | gr-qc |
Topology change in (2+1)-dimensional gravity with non-Abelian Higgs
field: We study topology change in (2+1)D gravity coupling with non-Abelian SO(2,1)
Higgs field from the point of view of Morse theory. It is shown that the Higgs
potential can be identified as a Morse function. The critical points of the
latter (i.e. loci of change of the spacetime topology) coincide with zeros of
the Higgs field. In these critical points two-dimensional metric becomes
degenerate, but the curvature remains bounded. | gr-qc |
Finite temperature applications in Gödel space-time: Temperature effects in a scalar field non-minimally coupled to gravity are
investigated. The Thermo Field Dynamics formalism is used. This is a
topological field theory that allows us to calculate different effects, such as
the Stefan-Boltzmann law and the Casimir effect, on an equal footing. These
phenomena are calculated assuming the G\"odel space-time as a gravitational
background. A possible implication of these results at the beginning of the
universe is discussed. | gr-qc |
Oddity in nonrelativistic, strong gravity: We consider the presence of odd powers of the speed of light $c$ in the
covariant nonrelativistic expansion of General Relativity (GR). The term of
order $c$ in the relativistic metric is a vector potential that contributes at
leading order in this expansion and describes strong gravitational effects
outside the (post-)Newtonian regime. The nonrelativistic theory of the leading
order potentials contains the full non-linear dynamics of the stationary sector
of GR. | gr-qc |
On a conformal Schwarzschild-de Sitter spacetime: On the basis of the C-metric, we investigate the conformal Schwarzschild -
deSitter spacetime and compute the source stress tensor and study its
properties, including the energy conditions. Then we study its extremal version
($b^{2} = 27m^{2}$, where $b$ is the deS radius and $m$ is the source mass),
when the metric is nonstatic. The weak-field version is analyzed in several
frames, and the metric becomes flat with the special choice $b = 1/a$, $a$
being the constant acceleration of the Schwarzschild-like mass or black hole.
This form is Rindler's geometry in disguise and is also conformal to a de
Sitter metric where the acceleration plays the role of the Hubble constant. In
its time dependent version, one finds that the proper acceleration of a static
observer is constant everywhere, in contrast with the standard Rindler case.
The timelike geodesics along the z-direction are calculated and proves to be
hyperbolae. | gr-qc |
Numerically generated quasi-equilibrium orbits of black holes: Circular
or eccentric?: We make a comparison between results from numerically generated,
quasi-equilibrium configurations of compact binary systems of black holes in
close orbits, and results from the post-Newtonian approximation. The
post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond
Newtonian gravity), and include rotational and spin-orbit effects, but are
generalized to permit orbits of non-zero eccentricity. Both treatments ignore
gravitational radiation reaction. The energy E and angular momentum J of a
given configuration are compared between the two methods as a function of the
orbital angular frequency \Omega. For small \Omega, corresponding to orbital
separations a factor of two larger than that of the innermost stable orbit, we
find that, if the orbit is permitted to be slightly eccentric, with e ranging
from \approx 0.03 to \approx 0.05, and with the two objects initially located
at the orbital apocenter (maximum separation), our PN formulae give much better
fits to the numerically generated data than do any circular-orbit PN methods,
including various ``effective one-body'' resummation techniques. We speculate
that the approximations made in solving the initial value equations of general
relativity numerically may introduce a spurious eccentricity into the orbits. | gr-qc |
On the Schroedinger Representation for a Scalar Field on Curved
Spacetime: It is generally known that linear (free) field theories are one of the few
QFT that are exactly soluble. In the Schroedinger functional description of a
scalar field on flat Minkowski spacetime and for flat embeddings, it is known
that the usual Fock representation is described by a Gaussian measure. In this
paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy
surface are considered. The classical structures relevant for quantization are
used for constructing the Schroedinger representation in the general case. It
is shown that in this case, the measure is also Gaussian. Possible implications
for the program of canonical quantization of midisuperspace models are pointed
out. | gr-qc |
Instability of Reissner-Nordström black hole in
Einstein-Maxwell-scalar theory: The scalarization of Reissner-Nordstr\"{o}m black holes was recently proposed
in the Einstein-Maxwell-scalar theory. Here, we show that the appearance of the
scalarized Reissner-Nordstr\"{o}m black hole is closely related to the
Gregory-Laflamme instability of the Reissner-Nordstr\"{o}m black hole without
scalar hair. | gr-qc |
Hamiltonian vs stability and application to Horndeski theory: A Hamiltonian density bounded from below implies that the lowest-energy state
is stable. We point out, contrary to common lore, that an unbounded Hamiltonian
density does not necessarily imply an instability: Stability is indeed a
coordinate-independent property, whereas the Hamiltonian density does depend on
the choice of coordinates. We discuss in detail the relation between the two,
starting from k-essence and extending our discussion to general field theories.
We give the correct stability criterion, using the relative orientation of the
causal cones for all propagating degrees of freedom. We then apply this
criterion to an exact Schwarzschild-de Sitter solution of a beyond-Horndeski
theory, while taking into account the recent experimental constraint regarding
the speed of gravitational waves. We extract the spin-2 and spin-0 causal cones
by analyzing respectively all the odd-parity and the $\ell = 0$ even-parity
modes. Contrary to a claim in the literature, we prove that this solution does
not exhibit any kinetic instability for a given range of parameters defining
the theory. | gr-qc |
Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames
of Minkowski Spacetime: II. Applications: Rotating Frames, Sagnac Effect,
Faraday Rotation, Wrap-up Effect: We apply the theory of non-inertial frames in Minkowski space-time, developed
in the previous paper, to various relevant physical systems. We give the 3+1
description without coordinate-singularities of the rotating disk and the
Sagnac effect, with added comments on pulsar magnetosphere and on a
relativistic extension of the Earth-fixed coordinate system. Then we study
properties of Maxwell equations in non-inertial frames like the wrap-up effect
and the Faraday rotation in astrophysics. | gr-qc |
Fully renormalized stress tensor correlator in flat space: We present a general procedure to renormalize the stress tensor two-point
correlation function on a Minkowski background in position space. The method is
shown in detail for the case of a free massive scalar field in the standard
Minkowski vacuum state, and explicit expressions are given for the counterterms
and finite parts, which are in full accordance with earlier results for the
massless case. For the general case in position space, only regularized --- but
not renormalized --- results have been obtained previously. After a Fourier
transformation to momentum space, we also check agreement with a previous
calculation there. We generalize our results to general Hadamard states.
Furthermore, the proposed procedure can presumably be generalized to the
important case of an inflationary spacetime background, where the transition to
momentum space is in general not possible. | gr-qc |
Supporting traversable wormholes: the case for noncommutative geometry: While wormholes may be just as good a prediction of Einstein's theory as
black holes, they are subject to severe restrictions from quantum field theory.
In particular, a wormhole can only be held open by violating the null energy
condition, calling for the existence of ``exotic matter," a condition that many
researchers consider completely unphysical, enough to rule out macroscopic
traversable wormholes. An equally serious problem is the enormous radial
tension at the throat of a typical Morris-Thorne wormhole unless the wormhole
has an extremely large throat size. It has been proposed that noncommutative
geometry, an offshoot of string theory, may be the proper tool for addressing
these issues. The purpose of this paper is two-fold: (1) to refine previous
arguments to make a stronger and more detailed case for this proposal and (2)
to obtain a complete wormhole solution from the given conditions. | gr-qc |
Quantum Nature of the Big Bang: An Analytical and Numerical
Investigation: Analytical and numerical methods are developed to analyze the quantum nature
of the big bang in the setting of loop quantum cosmology. They enable one to
explore the effects of quantum geometry both on the gravitational and matter
sectors and significantly extend the known results on the resolution of the big
bang singularity. Specifically, the following results are established for the
homogeneous isotropic model with a massless scalar field: i) the scalar field
is shown to serve as an internal clock, thereby providing a detailed
realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac
observables and semi-classical states are constructed rigorously; iii) the
Hamiltonian constraint is solved numerically to show that the big bang is
replaced by a big bounce. Thanks to the non-perturbative, background
independent methods, unlike in other approaches the quantum evolution is
deterministic across the deep Planck regime. Our constructions also provide a
conceptual framework and technical tools which can be used in more general
models. In this sense, they provide foundations for analyzing physical issues
associated with the Planck regime of loop quantum cosmology as a whole. | gr-qc |
Dynamics of $f(R)$ gravity models and asymmetry of time: We solve the field equations of modified gravity for $f(R)$ model in metric
formalism. Further, we obtain the fixed points of the dynamical system in phase
space analysis of $f(R)$ models, both with and without the effects of
radiation. Stability of these points is studied against perturbations in a
smooth spatial background by applying the conditions on the eigenvalues of the
matrix obtained in the linearized first-order differential equations. Following
this, these fixed points are used for analysing the dynamics of the system
during the radiation, matter and acceleration dominated phases of the universe.
Certain linear and quadratic forms of $f(R)$ are determined from the
geometrical and physical considerations and the behaviour of the scale factor
is found for those forms. Further, we also determine the Hubble parameter
$H(t)$, Ricci scalar $R$ for these cosmic phases. We show the emergence of an
asymmetry of time from the dynamics of the scalar field exclusively owing to
the $f(R)$ gravity in the Einstein frame that may lead to an arrow of time at a
classical level. | gr-qc |
Dynamical signature: complex manifolds, gauge fields and non-flat
tangent space: Theoretical possibilities of models of gravity with dynamical signature are
discussed. The different scenarios of the signature change are proposed in the
framework of Einstein-Cartan gravity. We consider, subsequently, the dynamical
signature in the model of the complex manifold with complex coordinates and
complex metric introduced, a complexification of the manifold and coordinates
through new gauge fields, an additional gauge symmetry for the Einsten-Cartan
vierbein fields and non-flat tangent space for the metric in the
Einstein-Cartan gravity. A new small parameter, which characterizes a degree of
the deviation of the signature from the background one, is introduced in all
models. The zero value of this parameter corresponds to the signature of an
initial background metric. In turn, in the models with gauge fields present,
this parameter represents a coupling constant of the gauge symmetry group. The
mechanism of metric's determination through induced gauge fields with defined
signature in the corresponding models is considered. The ways of the signature
change through the gauge fields dynamics are reviewed, the consequences and
applications of the proposed ideas are discussed as well. | gr-qc |
Ultimate fate of apparent horizons during a binary black hole merger II:
Horizons weaving back and forth in time: In this second part of a two-part paper, we discuss numerical simulations of
a head-on merger of two non-spinning black holes. We resolve the fate of the
original two apparent horizons by showing that after intersecting, their world
tubes "turn around" and continue backwards in time. Using the method presented
in the first paper to locate these surfaces, we resolve several such world
tubes evolving and connecting through various bifurcations and annihilations.
This also draws a consistent picture of the full merger in terms of apparent
horizons, or more generally, marginally outer trapped surfaces (MOTSs). The
MOTS stability operator provides a natural mechanism to identify MOTSs which
should be thought of as black hole boundaries. These are the two initial ones
and the final remnant. All other MOTSs lie in the interior and are neither
stable nor inner trapped. | gr-qc |
Cosmological Perturbations of Ultrarelativistic Plasmas: Scalar cosmological perturbations of a weakly self-interacting plasma mixed
with a perfect radiation fluid are investigated. Effects of this plasma are
considered through order $\lambda^{3/2}$ of perturbative thermal-field-theory
in the radiation dominated universe. The breakdown of thermal perturbation
theory at vastly subhorizon scales is circumvented by a Pad\'e approximant
solution. Compared to collisionless plasmas the phase speed and subhorizon
damping of the plasma density perturbations are changed. An example for a
self-interacting thermal field is provided by the neutrinos with effective
4-fermion interactions. | gr-qc |
Quintessence interacting dark energy from induced matter theory of
gravity: In the context of the induced matter theory of gravity, we investigate the
possibility of deriving a 4D quintessential scenario where an interaction
between dark energy and dark matter is allowed, and the dark energy component
is modeled by a minimally coupled scalar field. Regarding the Ponce de Leon
metric, we found that it is possible to obtain such scenario on which the
energy densities of dark matter and dark energy, are both depending of the
fifth extra coordinate. We obtain that the 4D induced scalar potential for the
quintessence scalar field, has the same algebraic form to the one found by
Zimdahl and Pavon in the context of usual 4D cosmology. | gr-qc |
Entropy bounds and nonlinear electrodynamics: Bekenstein's inequality sets a bound on the entropy of a charged macroscopic
body. Such a bound is understood as a universal relation between physical
quantities and fundamental constants of nature that should be valid for any
physical system. We reanalyze the steps that lead to this entropy bound
considering a charged object in conformity to Born-Infeld electrodynamics and
show that the bound depends of the underlying theory used to describe the
physical system. Our result shows that the nonlinear contribution to the
electrostatic self-energy causes a raise in the entropy bound. As an
intermediate step to obtain this result, we exhibit a general way to calculate
the form of the electric field for a given nonlinear electrodynamics in
Schwarzschild spacetime. | gr-qc |
Dark energy and accelerating cosmological evolution from osculating
Barthel-Kropina geometry: Finsler geometry is an important extension of Riemann geometry, in which to
each point of the spacetime manifold an arbitrary internal variable is
associated. Interesting Finsler geometries, with many physical applications,
are the Randers and Kropina type geometries, respectively. A subclass of
Finsler geometries is represented by the osculating Finsler spaces, in which
the internal variable is a function of the base manifold coordinates only. In
an osculating Finsler geometry one introduces the Barthel connection, which has
the remarkable property that it is the Levi-Civita connection of a Riemannian
metric. In the present work we consider the gravitational and cosmological
implications of a Barthel-Kropina type geometry. We assume that in this
geometry the Ricci type curvatures are related to the matter energy-momentum
tensor by the standard Einstein equations. The generalized Friedmann equations
in the Barthel-Kropina geometry are obtained by considering that the background
Riemannian metric is of Friedmann-Lemaitre-Robertson-Walker type. The matter
energy balance equation is also derived. The cosmological properties of the
model are investigated in detail, and it is shown that the model admits a de
Sitter type solution, and that an effective dark energy component can also be
generated. Several cosmological solutions are also obtained by numerically
integrating the generalized Friedmann equations. A comparison of two specific
classes of models with the observational data and with the standard
$\Lambda$CDM model is also performed, and it turns out that the Barthel-Kropina
type models give a satisfactory description of the observations. | gr-qc |
Gravitational lensing of wormholes in the galactic halo region: A recent study by Rahaman et al. has shown that the galactic halo possesses
the necessary properties for supporting traversable wormholes, based on two
observational results, the density profile due to Navarro et al. and the
observed flat rotation curves of galaxies. Using a method for calculating the
deflection angle pioneered by V. Bozza, it is shown that the deflection angle
diverges at the throat of the wormhole. The resulting photon sphere has a
radius of 0.40 ly. Given the dark-matter background, detection may be possible
from past data using ordinary light. | gr-qc |
A possible explanation of dark matter and dark energy involving a vector
torsion field: A simple gravitational model with torsion is studied, and it is suggested
that it could explain the dark matter and dark energy in the universe. It can
be reinterpreted as a model using the Einstein gravitational equations where
spacetime has regions filled with a perfect fluid with negative energy
(pressure) and positive mass density, other regions containing an anisotropic
substance that in the rest frame (where the momentum is zero) has negative mass
density and a uniaxial stress tensor, and possibly other "luminal" regions
where there is no rest frame. The torsion vector field is inhomogeneous
throughout spacetime, and possibly turbulent. Numerical simulations should
reveal whether or not the equations are consistent with cosmological
observations of dark matter and dark energy. | gr-qc |
Electromagnetic radiation due to naked singularity formation in
self-similar gravitational collapse: Dynamical evolution of test fields in background geometry with a naked
singularity is an important problem relevant to the Cauchy horizon instability
and the observational signatures different from black hole formation. In this
paper we study electromagnetic perturbations generated by a given current
distribution in collapsing matter under a spherically symmetric self-similar
background. Using the Green's function method, we construct the formula to
evaluate the outgoing energy flux observed at the future null infinity. The
contributions from "quasi-normal" modes of the self-similar system as well as
"high-frequency" waves are clarified. We find a characteristic power-law time
evolution of the outgoing energy flux which appears just before naked
singularity formation, and give the criteria as to whether or not the outgoing
energy flux diverges at the future Cauchy horizon. | gr-qc |
Casimir Tests of Scalar-Tensor Theories: We compute bounds and forecasts on screened modified gravity theories,
specialising to the chameleon model in Casimir force experiments. In
particular, we investigate the classical interaction between a plate and sphere
subject to a screened interaction of the chameleon type. We compare numerical
simulations of the field profile and the classical pressure exerted on the
sphere to analytical approximations for these non-linear field theories. In
particular, we focus on the proximity force approximation (PFA) and show that,
within the range of sphere sizes $R$ and plate-sphere distance $D$ simulated
numerically, the PFA does not reproduce the numerical results. This differs
from the case of linear field theories such as Newtonian gravity and a Yukawa
model where the PFA coincides with the exact results. We show that for
chameleon theories, the screening factor approximation (SFA) whereby the sphere
is modelled as a screened sphere embedded in the external field due to the
plates, fares better and can be used in the regime $D\gtrsim R$ to extract
constraints and forecasts from existing and forthcoming data. In particular, we
forecast that future Casimir experiments would corroborate the closing of the
parameter space for the simplest of chameleon models at the dark energy scale. | gr-qc |
Evaporation of a Kerr black hole by emission of scalar and higher spin
particles: We study the evolution of an evaporating rotating black hole, described by
the Kerr metric, which is emitting either solely massless scalar particles or a
mixture of massless scalar and nonzero spin particles. Allowing the hole to
radiate scalar particles increases the mass loss rate and decreases the angular
momentum loss rate relative to a black hole which is radiating nonzero spin
particles. The presence of scalar radiation can cause the evaporating hole to
asymptotically approach a state which is described by a nonzero value of $a_*
\equiv a / M$. This is contrary to the conventional view of black hole
evaporation, wherein all black holes spin down more rapidly than they lose
mass. A hole emitting solely scalar radiation will approach a final asymptotic
state described by $a_* \simeq 0.555$. A black hole that is emitting scalar
particles and a canonical set of nonzero spin particles (3 species of
neutrinos, a single photon species, and a single graviton species) will
asymptotically approach a nonzero value of $a_*$ only if there are at least 32
massless scalar fields. We also calculate the lifetime of a primordial black
hole that formed with a value of the rotation parameter $a_{*}$, the minimum
initial mass of a primordial black hole that is seen today with a rotation
parameter $a_{*}$, and the entropy of a black hole that is emitting scalar or
higher spin particles. | gr-qc |
A geometric perspective on singularity resolution and uniqueness in loop
quantum cosmology: We re-examine the issue of singularity resolution in homogeneous loop quantum
cosmology from the perspective of geometrical entities such as expansion rate
and the shear scalar. These quantities are very reliable measures of the
properties of spacetime and can be defined not only at the classical and
effective level, but also at an operator level in the quantum theory. From
their behavior in the effective constraint surface and in the effective loop
quantum spacetime, we show that one can severely restrict the ambiguities in
regularization of the quantum constraint and rule out unphysical choices. We
analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the
former case we show that the expansion rate is absolutely bounded only for the
so called improved quantization, a result which synergizes with uniqueness of
this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime,
we show that out of the available choices, the expansion rate and shear are
bounded for only one regularization of the quantum constraint. It turns out
that only for this choice, the theory exhibits quantum gravity corrections at a
unique scale, and is physically viable. | gr-qc |
Spherically symmetric Einstein-scalar-field equations for wave-like
decaying null infinity: We show that the spherically symmetric Einstein-scalar-field equations for
wave-like decaying initial data at null infinity have unique local solutions
and unique global solutions for small initial data. We also generalize
Christodoulou's global generalized solutions to the wave-like decaying initial
data. We emphasize that this decaying condition is sharp. | gr-qc |
2-2-holes simplified: Quadratic gravity illustrates how a replacement for black holes can emerge
from a UV completion of gravity. 2-2-holes are extremely compact horizonless
objects with an entropy $S_{22}$ due to trapped normal matter, and in this way
they are conceptually easy to understand. But the field equations are
cumbersome and the numerical analysis has so far been restricted to relatively
small size solutions. Here we show how the properties of arbitrarily large
2-2-holes can be found, including the time delay for gravitational wave echoes
and the result $T_\infty S_{22}=M/2$. The starting point is to formulate the
metric in terms of the tortoise coordinate, and to have one of the two metric
functions be a conformal factor. A large conformally-related volume becomes
associated with the interior of a 2-2-hole. We also discuss implications for
the weak gravity conjecture. | gr-qc |
Dominant property for the Bel-Robinson tensor and tensor S: The Bel-Robinson tensor contains many nice mathematical properties and its
dominant energy condition is desirable for describing the positive
gravitational energy. The dominant property is a basic requirement for the
quasi-local mass, i.e., in small sphere limit. We claim that there exists
another option, a linear combination between the Bel-Robinson tensor $B$ and
tensor $S$, which contributes the same dominant property. Moreover, using the 5
Petrov types as the verification, we found that this dominant property
justification for the Bel-Robinson tensor can be simplified as examining
$B_{0000}\geq|B_{\alpha\beta{}00}|$ and $B_{0000}\geq|B_{0123}|$, instead of
$B_{0000}\geq|B_{\alpha\beta\lambda\sigma}|$ for all
$\alpha,\beta,\lambda,\sigma=0,1,2,3$. | gr-qc |
Superradiance and Stability of Kerr Black Hole Enclosed by Anisotropic
Fluid Matter: Focusing on the rotating black hole (BH) surrounded by the anisotropic fluid
matters; radiation, dust, and dark matter, we study the massive scalar
superradiant scattering and the stability in the Kiselev spacetime.
Superradiance behavior is dependent on the intensity parameter of the
anisotropic matter $K$ in the Kiselev spacetime. By adopting the manifest of
low-frequency and low-mass for the scalar perturbation, we find $K<0$ enhances
the superradiance scattering within the broader frequency range, compared to
$K=0$ while $K>0$ suppresses within the narrower frequency range. As a result,
the radiation and dark matter around the rotating BH act as amplifier and
attenuator for the massive scalar superradiance, respectively. This is while
the dust has a twofold role because of admitting both signs of $K$. Through
stability analysis in the light of the BH bomb mechanism, we show in the
presence of dark matter, the instability regime of standard Kerr BH ($K=0$)
gets improved in favor of stabilization while the radiation and dust do not
affect it. In other words, by taking the dark matter fluid around BH into
account, we obtain a broader regime that allows the massive scalar field
dynamic to enjoy superradiant stability. | gr-qc |
Testing the Master Constraint Programme for Loop Quantum Gravity IV.
Free Field Theories: This is the fourth paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. We now move on to free field theories with constraints, namely Maxwell
theory and linearized gravity. Since the Master constraint involves squares of
constraint operator valued distributions, one has to be very careful in doing
that and we will see that the full flexibility of the Master Constraint
Programme must be exploited in order to arrive at sensible results. | gr-qc |
Hair mass bound in the black hole with nonzero cosmological constants: We study mass bounds of Maxwell fields in RN black holes and genuine hair in
Einstein-Born-Infeld black holes with various cosmological constants. It shows
that the Maxwell field serves as a good probe to disclose the hair distribution
described with the event horizon and the photonsphere. And we find that the
Hod's lower bound obtained in asymptotically flat space also holds in the
asymptotically dS Einstein-Born-Infeld hairy black holes. In contrast, the
Hod's lower bound can be invaded in the asymptotically AdS Einstein-Born-Infeld
hairy black holes. It implies that the AdS boundary could make the Born-Infeld
hair easier to condense in the near horizon area. | gr-qc |
Seeing Relativity -- III. Journeying within the Kerr metric toward the
negative gravity region: In this paper we study some features of the Kerr metric both from an analytic
and a visual point of view by performing accurate raytracing in various
situations. We focus on features that are unique to the maximal analytic
extension of the Kerr metric as compared to that of the Schwarzschild or even
the Reissner-Nordstr\"om one. A large number of new, yet underexplored
phenomena appear, especially regarding the structure of bounded null geodesics
and the aspect of the negative gravity regions whose visual characteristics are
shown both from outside and inside it. | gr-qc |
Malaise and remedy of binary boson-star initial data: Through numerical simulations of boson-star head-on collisions, we explore
the quality of binary initial data obtained from the superposition of
single-star spacetimes. Our results demonstrate that evolutions starting from a
plain superposition of individual boosted boson-star spacetimes are vulnerable
to significant unphysical artefacts. These difficulties can be overcome with a
simple modification of the initial data suggested in [PRD 99 (2018) 044046] for
collisions of oscillatons. While we specifically consider massive complex
scalar field boson star models up to a 6th-order-polynomial potential, we argue
that this vulnerability is universal and present in other kinds of exotic
compact systems and hence needs to be addressed. | gr-qc |
Thick domain walls around a black hole: We discuss the gravitationally interacting system of a thick domain wall and
a black hole. We numerically solve the scalar field equation in the
Schwarzschild spacetime and obtain a sequence of static axi-symmetric solutions
representing thick domain walls. We find that, for the walls near the horizon,
the Nambu--Goto approximation is no longer valid. | gr-qc |
Compact stars in Eddington-inspired Born-Infeld gravity: Anomalies
associated with phase transitions: We study how generic phase transitions taking place in compact stars
constructed in the framework of the Eddington-inspired Born-Infeld (EiBI)
gravity can lead to anomalous behavior of these stars. For the case with
first-order phase transitions, compact stars in EiBI gravity with a positive
coupling parameter $\kappa $ exhibit a finite region with constant pressure,
which is absent in general relativity. However, for the case with a negative
$\kappa $, an equilibrium stellar configuration cannot be constructed. Hence,
EiBI gravity seems to impose stricter constraints on the microphysics of
stellar matter. Besides, in the presence of spatial discontinuities in the
sound speed $c_s$ due to phase transitions, the Ricci scalar is spatially
discontinuous and contains $\delta$-function singularities proportional to the
jump in $c_s^2$ acquired in the associated phase transition. | gr-qc |
Canonical structure of minimal varying $Λ$ theories: Minimal varying $\Lambda$ theories are defined by an action built from the
Einstein-Cartan-Holst first order action for gravity with the cosmological
constant $\Lambda$ as an independent scalar field, and supplemented by the
Euler and Pontryagin densities multiplied by $1/\Lambda$. We identify the
canonical structure of these theories which turn out to represent an example of
irregular systems. We find five degrees of freedom on generic backgrounds and
for generic values of parameters, whereas if the parameters satisfy a certain
condition (which includes the most commonly considered Euler case) only three
degrees of freedom remain. On de Sitter-like backgrounds the canonical
structure changes, and due to an emergent conformal symmetry one degree of
freedom drops from the spectrum. We also analyze the self-dual case with an
holomorphic action depending only on the self-dual part of the connection. In
this case we find two (complex) degrees of freedom, and further discuss the
Kodama state, the restriction to de Sitter background and the effect of reality
conditions. | gr-qc |
Variations of the Energy of Free Particles in the pp-Wave Spacetimes: We consider the action of exact plane gravitational waves, or pp-waves, on
free particles. The analysis is carried out by investigating the variations of
the geodesic trajectories of the particles, before and after the passage of the
wave. The initial velocities of the particles are non-vanishing. We evaluate
numerically the Kinetic energy per unit mass of the free particles, and obtain
interesting, quasi-periodic behaviour of the variations of the Kinetic energy
with respect to the width $\lambda$ of the gaussian that represents the wave.
The variation of the energy of the free particle is expected to be exactly
minus the variation of the energy of the gravitational field, and therefore
provides an estimation of the local variation of the gravitational energy. The
investigation is carried out in the context of short bursts of gravitational
waves, and of waves described by normalised gaussians, that yield impulsive
waves in a certain limit. | gr-qc |
New Insights into the Nature of Nonlinear Gravitational Waves: We study the evolution equations for gravitational waves, which are derived
using the full metric to raise and lower indices. This method ensures full
consistency between the Ricci tensor and all gauge restrictions and
requirements, and allows a meaningful expansion of all tensors up to second
order, avoiding several inconsistencies and contradictions observed in previous
work. Taking the harmonic gauge to second order in the perturbation theory
results in a new nonlinear equation. We show that non-trivial solutions to this
equation are necessarily non-plane wave modes with a non-zero trace. These
solutions must contain both longitudinal and transverse components, as both are
permitted by the gauge restrictions. | gr-qc |
Maxwell equations in curved spacetime: In curved spacetime, Maxwell's equations can be expressed in forms valid in
Minkowski background, with the effect of the metric (gravity) appearing as
effective polarizations and magnetizations. The electric and magnetic (EM)
fields depend on the observer's frame four-vector. We derive Maxwell's
equations valid in general curved spacetime using the fields defined in the
normal frame, the coordinate frame, and two other non-covariant methods used in
the literature. By analyzing the case in the generic frame we show that the EM
fields, as well as the charge and current densities, defined in non-covariant
ways do not correspond to physical ones measured by an observer. We show that
modification of the homogeneous part is inevitable to any observer, and such a
modification is difficult to interpret as the effective medium property. The
normal frame is the relevant one to use as it gives the EM fields measured by
an Eulerian observer. | gr-qc |
Ghost and tachyon free Poincaré gauge theories: a systematic approach: A systematic method is presented for determining the conditions on the
parameters in the action of a parity-preserving gauge theory of gravity for it
to contain no ghost or tachyon particles. The technique naturally accommodates
critical cases in which the parameter values lead to additional gauge
invariances. The method is implemented as a computer program, and is used here
to investigate the particle content of parity-conserving Poincar\'e gauge
theory, which we compare with previous results in the literature. We find 450
critical cases that are free of ghosts and tachyons, and we further identify 10
of these that are also power-counting renormalizable, of which four have only
massless tordion propagating particles and the remaining six have only a
massive tordion propagating mode. | gr-qc |
On Signature Transition and Compactification in Kaluza-Klein Cosmology: We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative
cosmological constant and a Robertson-Walker type metric. It is shown that the
solutions to Einstein field equations have degenerate metric and exhibit
transitioins from a Euclidean to a Lorentzian domain. We then suggest a
mechanism, based on signature transition which leads to compactification of the
internal space in the Lorentzian region as $a \sim |\Lambda|^{1/2}$. With the
assumption of a very small value for the cosmological constant we find that the
size of the universe $R$ and the internal scale factor $a$ would be related
according to $Ra\sim 1$ in the Lorentzian region. The corresponding
Wheeler-DeWitt equation has exact solution in the mini-superspace giving rise
to a quantum state which peaks in the vicinity of the classical solutions
undergoing signature transition. | gr-qc |
Resolution of cosmological singularity in Hořava-Lifshitz cosmology: The standard $\Lambda$CDM model despite its agreement with observational data
still has some issues unaddressed, lie the problem of initial singularity.
Solving that problem usually requires modifications of general relativity.
However, there appeared the Ho\v{r}ava-Lifshitz (HL) theory of gravity, in
which equations governing cosmological evolution include a new term scaling
similarly as dark radiation term in the Friedmann equations, enabling a bounce
of the universe instead of initial singularity. This review describes past
works on a stability of such a bounce in different formulations of HL theory,
initial detailed balance scenario and further projectable versions containing
higher than quadratic term to the original action. | gr-qc |
Creating spacetime shortcuts with gravitational waveforms: A region-delimited gravitational wave field can be constructed, such that a
subset of geodesics crossing this region will move faster than nearby geodesics
moving entirely inside flat spacetime, along a preferred direction. Null
geodesics inside this region will move faster-than-light according to far away
observers. The waveform is synthesized from homogeneous plane wave solutions,
and the resulting field is the gravitational equivalent of a Gaussian beam. | gr-qc |
On quantum superpositions of graphs, no-signalling and covariance: We provide a mathematically and conceptually robust notion of quantum
superpositions of graphs. We argue that, crucially, quantum superpositions of
graphs require node names for their correct alignment, which we demonstrate
through a no-signalling argument. Nevertheless, node names are a fiducial
construct, serving a similar purpose to the labelling of points through a
choice of coordinates in continuous space. Graph renamings, aka isomorphisms,
are understood as a change of coordinates on the graph and correspond to a
natively discrete analogue of continuous diffeomorphisms. We postulate renaming
invariance as a symmetry principle in discrete topology of similar weight to
diffeomorphism invariance in the continuous. We explain how to impose renaming
invariance at the level of quantum superpositions of graphs, in a way that
still allows us to talk about an observable centred at a specific node. | gr-qc |
Gravitational bending angle of light for finite distance and the
Gauss-Bonnet theorem: We discuss a possible extension of calculations of the bending angle of light
in a static, spherically symmetric and asymptotically flat spacetime to a
non-asymptotically flat case. We examine a relation between the bending angle
of light and the Gauss-Bonnet theorem by using the optical metric. A
correspondence between the deflection angle of light and the surface integral
of the Gaussian curvature may allow us to take account of the finite distance
from a lens object to a light source and a receiver. Using this relation, we
propose a method for calculating the bending angle of light for such cases.
Finally, this method is applied to two examples of the non-asymptotically flat
spacetimes to suggest finite-distance corrections: Kottler (Schwarzschild-de
Sitter) solution to the Einstein equation and an exact solution in Weyl
conformal gravity. | gr-qc |
Re-Scaling of Energy in the Stringy Charged Black Hole Solutions using
Approximate Symmetries: This paper is devoted to study the energy problem in general relativity using
approximate Lie symmetry methods for differential equations. We evaluate
second-order approximate symmetries of the geodesic equations for the stringy
charged black hole solutions. It is concluded that energy must be re-scaled by
some factor in the second-order approximation. | gr-qc |
A New Unified Theory of Electromagnetic and Gravitational Interactions: In this paper we present a new unified theory of electromagnetic and
gravitational interactions. By considering a four-dimensional spacetime as a
hypersurface embedded in a five-dimensional bulk spacetime, we derive the
complete set of field equations in the four-dimensional spacetime from the
five-dimensional Einstein field equation. Besides the Einstein field equation
in the four-dimensional spacetime, an electromagnetic field equation is
derived: $\nabla_a F^{ab}-\xi R^b_{\;\,a}A^a=-4\pi J^b$ with $\xi=-2$, where
$F^{ab}$ is the antisymmetric electromagnetic field tensor defined by the
potential vector $A^a$, $R_{ab}$ is the Ricci curvature tensor of the
hypersurface, and $J^a$ is the electric current density vector. The
electromagnetic field equation differs from the Einstein-Maxwell equation by a
curvature-coupled term $\xi R^b_{\;\,a}A^a$, whose presence addresses the
problem of incompatibility of the Einstein-Maxwell equation with a universe
containing a uniformly distributed net charge as discussed in a previous paper
by the author [L.-X. Li, Gen. Relativ. Gravit. {\bf 48}, 28 (2016)]. Hence, the
new unified theory is physically different from the Kaluza-Klein theory and its
variants where the Einstein-Maxwell equation is derived. In the
four-dimensional Einstein field equation derived in the new theory, the source
term includes the stress-energy tensor of electromagnetic fields as well as the
stress-energy tensor of other unidentified matter. Under some conditions the
unidentified matter can be interpreted as a cosmological constant in the
four-dimensional spacetime. We argue that, the electromagnetic field equation
and hence the unified theory presented in this paper can be tested in an
environment with a high mass density, e.g., inside a neutron star or a white
dwarf, and in the early epoch of the universe. | gr-qc |
On the stability of the cosmological solutions in f(R,G) gravity: Modified gravity is one of the most promising candidates for explaining the
current accelerating expansion of the Universe, and even its unification with
the inflationary epoch. Nevertheless, the wide range of models capable to
explain the phenomena of dark energy, imposes that current research focuses on
a more precise study of the possible effects of modified gravity may have on
both cosmological and local levels. In this paper, we focus on the analysis of
a type of modified gravity, the so-called f(R,G) gravity and we perform a deep
analysis on the stability of important cosmological solutions. This not only
can help to constrain the form of the gravitational action, but also facilitate
a better understanding of the behavior of the perturbations in this class of
higher order theories of gravity, which will lead to a more precise analysis of
the full spectrum of cosmological perturbations in future. | gr-qc |
On the instability of charged wormholes supported by a ghost scalar
field: In previous work, we analyzed the linear and nonlinear stability of static,
spherically symmetric wormhole solutions to Einstein's field equations coupled
to a massless ghost scalar field. Our analysis revealed that all these
solutions are unstable with respect to linear and nonlinear spherically
symmetric perturbations and showed that the perturbation causes the wormholes
to either decay to a Schwarzschild black hole or undergo a rapid expansion.
Here, we consider charged generalization of the previous models by adding to
the gravitational and ghost scalar field an electromagnetic one. We first
derive the most general static, spherically symmetric wormholes in this theory
and show that they give rise to a four-parameter family of solutions. This
family can be naturally divided into subcritical, critical and supercritical
solutions depending on the sign of the sum of the asymptotic masses. Then, we
analyze the linear stability of these solutions. We prove that all subcritical
and all critical solutions possess one exponentially in time growing mode. It
follows that all subcritical and critical wormholes are linearly unstable. In
the supercritical case we provide numerical evidence for the existence of a
similar unstable mode. | gr-qc |
Proof of the Einstein quadrupole formula for solutions of the
Einstein-Vlasov system close to Minkowski spacetime: We rigorously derive the quadrupole formula within the context of the
Einstein-Vlasov system. The main contribution of this work is an estimate of
the remainder terms, derived from well-defined assumptions, with explicitly
stated error terms that depend on the solution's boundedness and decay
properties, and the distance to the source. The assumptions are linked to
established properties of global solutions of the Einstein-Vlasov system as in
\cite{LT}. Prior derivations of the quadrupole formula have relied on
post-Newtonian analysis and lacked comparisons with global solution properties.
The importance of the no-incoming-radiation condition is emphasized
underscoring the need for solutions satisfying this condition. This work thus
addresses the limitations of existing results and provides motivation for
further research on global solution properties of the Einstein-Vlasov system. | gr-qc |
Singularity avoidance in Bianchi I quantum cosmology: We extend recent discussions of singularity avoidance in quantum gravity from
isotropic to anisotropic cosmological models. The investigation is done in the
framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate
criteria of singularity avoidance for general Bianchi class A models and give
explicit and detailed results for Bianchi I models with and without matter. We
find that the classical singularities can generally be avoided in these models. | gr-qc |
Relaxation-Time Model for the Post-Newtonian Boltzmann Equation: The non-equilibrium contributions to the post-Newtonian hydrodynamic
equations are determined from a relaxation-time model of the post-Newtonian
Boltzmann equation. The Chapman-Enskog method is used to calculate the
non-equilibrium distribution function. The components of the energy-momentum
tensor are found from the knowledge of the non-equilibrium and the
post-Newtonian equilibrium Maxwell-J\"uttner distribution functions. The
linearized field equations for the mass, momentum and internal energy densities
coupled with the three Poisson equations of the post-Newtonian approximation
are investigated by considering a plane wave representation of the fields. The
constitutive equations for the viscous stress and heat flux vector are obtained
and it is shown that the transport coefficients of shear viscosity and heat
conductivity do depend on the Newtonian gravitational potential. | gr-qc |
The magnetic Rayleigh-Taylor instability around astrophysical black
holes: We investigate the development of the magnetic Rayleigh-Taylor instability at
the inner edge of an astrophysical disk around a spinning central black hole.
We solve the equations of general relativity that govern small amplitude
oscillations of a discontinuous interface in a Keplerian disk threaded by an
ordered magnetic field, and we derive a stability criterion that depends on the
central black hole spin and the accumulated magnetic field. We also compare our
results with the results of GR MHD simulations of black hole accretion flows
that reach a magnetically arrested state (MAD). We found that the instability
growth timescales that correspond to the simulation parameters are comparable
to the corresponding timescales for free-fall accretion from the ISCO onto the
black hole. We thus propose that the Rayleigh-Taylor instability disrupts the
accumulation of magnetic flux onto the black hole horizon as the disk reaches a
MAD state. | gr-qc |
Towards degeneracy breaking of early universe models: There are many possibilities of scenarios in the early universe, which can
give rise to the same observational signals due to the degeneracy among each
other, caused by equivalence under the conformal transformations. In order to
break the degeneracy, in this paper we take into account the so-called
"frame-invariant variables" proposed by A. Ijjas and P. J. Steinhardt in
\cite{Ijjas:2015zma}. We discuss how the different scenarios will distribute in
different parametric space constructed from those variables, waiting for the
judgement of real observations in the future. Several concrete models with
explicit non-minimal coupling functions are also discussed. | gr-qc |
Entropy of Kerr--Newman--AdS black holes with torsion: The canonical approach to black hole entropy in Poincar\'e gauge theory
without matter is extended to include Maxwell field as a matter source. The new
formalism is used to calculate asymptotic charges and entropy of
Kerr--Newmann--AdS black holes with torsion. The result implies that the first
law, with a nontrivial contribution of the Maxwell field, takes the same form
as in general relativity. | gr-qc |
Gravitational Wave Memory: A New Approach to Study Modified Gravity: It is well known that two types of gravitational wave memory exist in general
relativity (GR): the linear memory and the non-linear, or Christodoulou memory.
These effects, especially the latter, depend on the specific form of Einstein
equation. It can then be speculated that in modified theories of gravity, the
memory can differ from the GR prediction, and provides novel phenomena to study
these theories. We support this speculation by considering scalar-tensor
theories, for which we find two new types of memory: the T memory and the S
memory, which contribute to the tensor and scalar components of gravitational
wave, respectively. In particular, the former is caused by the burst of energy
carried away by scalar radiation, while the latter is intimately related to the
no scalar hair property of black holes in scalar-tensor gravity. We estimate
the size of these two types of memory in gravitational collapses, and formulate
a detection strategy for the S memory, which can be singled out from tensor
gravitational waves. We show that (i) the S memory exists even in spherical
symmetry, and is observable under current model constraints, and (ii) while the
T memory is usually much weaker than the S memory, it can become comparable in
the case of spontaneous scalarization. | gr-qc |
Gravitational radiation from binary systems in $f(R)$ gravity: A
semi-classical approach: The rate of energy loss and orbital period decay of quasi-stable compact
binary systems are derived in $f(R)$ theory of gravity using the method of a
single vertex graviton emission process from a classical source. After
linearising the $f(R)$ action written in an equivalent scalar-tensor format in
the Einstein frame, we identify the appropriate interaction terms between the
massless spin-2 tensor mode, massive scalar mode, and the energy momentum
tensor. The definition of the scalar field is related to the $f(R)$ models.
Then using the interaction vertex we compute the rate of energy loss due to
spin-2 quadrupole radiation, which comes out to be the same as the
Peter-Mathews formula with a multiplication factor, and also the energy loss
due to the scalar dipole radiation. The total energy loss is the sum of these
two contributions. Our derivation is most general as it is applicable for both
arbitrary eccentricity of the binary orbits and arbitrary mass of the scalar
field. Using the derived theoretical formula for the period decay of the binary
systems, we compare the predictions of $f(R)$ gravity and general relativity
for the observations of four binary systems, i.e. Hulse-Taylor Binary, PSR
J1141-6545, PSR J1738+0333, and PSR J0348+0432. Thus we put bound on three
well-known $f(R)$ dark energy models, namely the Hu-Sawicki, the Starobinsky,
and the Tsujikawa model. We get the best constraint on $f'(R_0)-1$ (where $R_0$
is the scalar curvature of the Universe at the present epoch) from the
Tsujikawa model, i.e $\vert f'(R_0)-1\vert < 2.09\times 10^{-4}$. This bound is
stronger than those from most of the astrophysical observations and even some
cosmological observations. | gr-qc |
Motion in classical field theories and the foundations of the self-force
problem: This article serves as a pedagogical introduction to the problem of motion in
classical field theories. The primary focus is on self-interaction: How does an
object's own field affect its motion? General laws governing the self-force and
self-torque are derived using simple, non-perturbative arguments. The relevant
concepts are developed gradually by considering motion in a series of
increasingly complicated theories. Newtonian gravity is discussed first, then
Klein-Gordon theory, electromagnetism, and finally general relativity. Linear
and angular momenta as well as centers of mass are defined in each of these
cases. Multipole expansions for the force and torque are then derived to all
orders for arbitrarily self-interacting extended objects. These expansions are
found to be structurally identical to the laws of motion satisfied by extended
test bodies, except that all relevant fields are replaced by effective versions
which exclude the self-fields in a particular sense. Regularization methods
traditionally associated with self-interacting point particles arise as
straightforward perturbative limits of these (more fundamental) results.
Additionally, generic mechanisms are discussed which dynamically shift ---
i.e., renormalize --- the apparent multipole moments associated with
self-interacting extended bodies. Although this is primarily a synthesis of
earlier work, several new results and interpretations are included as well. | gr-qc |
A physics-informed search for metric solutions to Ricci flow, their
embeddings, and visualisation: Neural networks with PDEs embedded in their loss functions (physics-informed
neural networks) are employed as a function approximators to find solutions to
the Ricci flow (a curvature based evolution) of Riemannian metrics. A general
method is developed and applied to the real torus. The validity of the solution
is verified by comparing the time evolution of scalar curvature with that found
using a standard PDE solver, which decreases to a constant value of 0 on the
whole manifold. We also consider certain solitonic solutions to the Ricci flow
equation in two real dimensions. We create visualisations of the flow by
utilising an embedding into $\mathbb{R}^3$. Snapshots of highly accurate
numerical evolution of the toroidal metric over time are reported. We provide
guidelines on applications of this methodology to the problem of determining
Ricci flat Calabi--Yau metrics in the context of String theory, a long standing
problem in complex geometry. | gr-qc |
Convergence of Fourier-domain templates for inspiraling eccentric
compact binaries: The space-based detector LISA may observe gravitational waves from the early
inspiral of stellar-mass black hole binaries, some of which could have
significant eccentricity. Current gravitational waveform templates are only
valid for small orbital velocities (i.e., in a post-Newtonian expansion) and
small initial eccentricity $e_0$ ("post-circular" expansion). We conventionally
define $e_0$ as the eccentricity corresponding to an orbital frequency of $5
\text{ mHz}$, and we study the convergence properties of frequency-domain
inspiral templates that are accurate up to 2PN and order $e_0^6$ in
eccentricity. We compute the so-called "unfaithfulness" between the full
template and "reduced" templates obtained by dropping some terms in the phasing
series; we investigate the conditions under which systematic errors are
negligible with respect to statistical errors, and we study the convergence
properties of statistical errors. In general, eccentric waveforms lead to
larger statistical errors than circular waveforms due to correlations between
the parameters, but the error estimates do not change significantly as long as
we include terms of order $e_0^2$ or higher in the phasing. | gr-qc |
Geometry of Vaidya spacetimes: We investigate the geometrical structure of Vaidya's spacetime in the case of
a white hole with decreasing mass, stabilising to a black hole in finite or
infinite time or evaporating completely. Our approach relies on a detailed
analysis of the ordinary differential equation describing the incoming
principal null geodesics, among which are the generators of the past horizon.
We devote special attention to the case of a complete evaporation in infinite
time and establish the existence of an asymptotic light-like singularity of the
conformal curvature, touching both the past space-like singularity and future
time-like infinity. This singularity is present independently of the decay rate
of the mass. We derive an explicit formula that relates directly the strength
of this null singularity to the asymptotic behaviour of the mass function. | gr-qc |
Stability analysis and Observational Measurement in Chameleonic
Generalised Brans--Dicke Cosmology: We investigate the dynamics of the chameleonic Generalised Brans--Dicke model
in flat FRW cosmology. In a new approach, a framework to study stability and
attractor solutions in the phase space is developed for the model by
simultaneously best fitting the stability and model parameters with the
observational data. The results show that for an accelerating universe the
phantom crossing does not occur in the past and near future. | gr-qc |
Violent nonlinear collapse in the interior of charged hairy black holes: We construct a new one-parameter family indexed by $\epsilon$ of two-ended,
spatially-homogeneous black hole interiors solving the
Einstein-Maxwell-Klein-Gordon equations with a (possibly zero) cosmological
constant $\Lambda$ and bifurcating off a Reissner-Nordstr\"om-(dS/AdS) interior
($\epsilon = 0$). For all small $\epsilon \neq 0$, we prove that, although the
black hole is charged, its terminal boundary is an everywhere-spacelike Kasner
singularity foliated by spheres of zero radius $r$.
Moreover, smaller perturbations (i.e. smaller $|\epsilon|$) are more singular
than larger one, in the sense that the Hawking mass and the curvature blow up
following a power law of the form $r^{-O(\epsilon^{-2})}$ at the singularity
$\{r=0\}$. This unusual property originates from a dynamical phenomenon --
violent nonlinear collapse -- caused by the almost formation of a Cauchy
horizon to the past of the spacelike singularity $\{r=0\}$. This phenomenon was
previously described numerically in the physics literature and referred to as
"the collapse of the Einstein-Rosen bridge".
While we cover all values of $\Lambda \in \mathbb{R}$, the case $\Lambda< 0$
is of particular significance to the AdS/CFT correspondence. Our result can
also be viewed in general as a first step towards the understanding of the
interior of hairy black holes. | gr-qc |
Thermodynamics of phantom Reissner-Nordstrom-AdS black hole: We obtain a new solution of the Einstein-anti-Maxwell theory with
cosmological constant, called anti-Reissner-Nordstrom-(A)de Sitter
(anti-RN-(A)dS) solution. The basic properties of this solution is reviewed.
Its thermodynamics is consistently established, with the extreme cases and
phase transitions, where the analysis is performed through two methods, the
usual one and that of Geometrothermodynamics . The Geometrothermodynamics
analysis does not provide a result in agreement with the usual method or by the
specific heat. We establish local and global thermodynamic stabilities of
anti-RN-AdS solution through the specific heat and the canonical and
grand-canonical ensembles. | gr-qc |
Computer Algebra Solving of Second Order ODEs Using Symmetry Methods: An update of the ODEtools Maple package, for the analytical solving of 1st
and 2nd order ODEs using Lie group symmetry methods, is presented. The set of
routines includes an ODE-solver and user-level commands realizing most of the
relevant steps of the symmetry scheme. The package also includes commands for
testing the returned results, and for classifying 1st and 2nd order ODEs. | gr-qc |
Critical Phenomena Inside Global Monopoles: The gravitational collapse of a triplet scalar field is examined assuming a
hedgehog ansatz for the scalar field. Whereas the seminal work by Choptuik with
a single, strictly spherically symmetric scalar field found a discretely
self-similar (DSS) solution at criticality with echoing period $\Delta=3.44$,
here a new DSS solution is found with period $\Delta=0.46$. This new critical
solution is also observed in the presence of a symmetry breaking potential as
well as within a global monopole. The triplet scalar field model contains
Choptuik's original model in a certain region of parameter space, and hence his
original DSS solution is also a solution. However, the choice of a hedgehog
ansatz appears to exclude the original DSS. | gr-qc |
Cosmological implications of an evolutionary quantum gravity: The cosmological implications of an evolutionary quantum gravity are analyzed
in the context of a generic inhomogeneous model. The Schr\"{o}dinger problem is
formulated and solved in the presence of a scalar field, an ultrarelativistic
matter and a perfect gas regarded as the dust-clock. Considering the actual
phenomenology, it is shown how the evolutionary approach overlaps the
Wheeler-DeWitt one. | gr-qc |
The Universal Property of the Entropy Sum of Black Holes in All
Dimensions: It is proposed by Cvetic et al [Phys. Rev. Lett. 106 (2011) 121301] that the
product of all horizon areas for general rotating multi-change black holes has
universal expressions independent of the mass. When we consider the product of
all horizon entropies, however, the mass will be present in some cases, while
another new universal property [JHEP 1401 (2014) 031] is preserved, which is
more general and says that the sum of all horizon entropies depends only on the
coupling constants of the theory and the topology of the black hole. The
property has been studied in limited dimensions and the generalization in
arbitrary dimensions is not straight-forward. In this Letter, we prove a useful
formula, which makes it possible to investigate this conjectured universality
in arbitrary dimensions for the maximally symmetric black holes in general
Lovelock gravity and $f(R)$ gravity. We also propose an approach to compute the
entropy sum of general Kerr-(anti-)de-Sitter black holes in arbitrary
dimensions. In all these cases, we prove that the entropy sum only depends on
the coupling constants and the topology of the black hole. | gr-qc |
On the viability of the Palatini form of 1/R gravity: Recently Flanagan [astro-ph/0308111] has argued that the Palatini form of 1/R
gravity is ruled out by experiments such as electron-electron scattering. His
argument involves adding minimally coupled fermions in the Jordan frame and
transforming to the Einstein frame. This produces additional terms that are
ruled out experimentally.
Here I argue that this conclusion is false. It is well known that conformally
related theories are mathematically equivalent but not physically equivalent.
As discussed by Magnano and Sokolowski [2] one must decide, in the vacuum
theory, which frame is the physical frame and add the minimally coupled
Lagrangian in this frame. If this procedure is followed the resulting theory is
not ruled out experimentally. The discussions in this paper also show that the
equivalence between the generalized gravitational theories and scalar tensor
theories discussed by Flanagan [gr-qc/0309015] is only mathematical, not
physical. | gr-qc |
Black Holes and String Theory: This is a short summary of my lectures given at the Fourth Mexican School on
Gravitation and Mathematical Physics. These lectures gave a brief introduction
to black holes in string theory, in which I primarily focussed on describing
some of the recent calculations of black hole entropy using the statistical
mechanics of D-brane states. The following overview will also provide the
interested students with an introduction to the relevant literature. | gr-qc |
Fate of the first traversible wormhole: black-hole collapse or
inflationary expansion: We study numerically the stability of Morris & Thorne's first traversible
wormhole, shown previously by Ellis to be a solution for a massless ghost
Klein-Gordon field. Our code uses a dual-null formulation for spherically
symmetric space-time integration, and the numerical range covers both universes
connected by the wormhole. We observe that the wormhole is unstable against
Gaussian pulses in either exotic or normal massless Klein-Gordon fields. The
wormhole throat suffers a bifurcation of horizons and either explodes to form
an inflationary universe or collapses to a black hole, if the total input
energy is respectively negative or positive. As the perturbations become small
in total energy, there is evidence for critical solutions with a certain
black-hole mass or Hubble constant. The collapse time is related to the initial
energy with an apparently universal critical exponent. For normal matter, such
as a traveller traversing the wormhole, collapse to a black hole always
results. However, carefully balanced additional ghost radiation can maintain
the wormhole for a limited time. The black-hole formation from a traversible
wormhole confirms the recently proposed duality between them. The inflationary
case provides a mechanism for inflating, to macroscopic size, a Planck-sized
wormhole formed in space-time foam. | gr-qc |
Local properties and global structure of McVittie spacetimes with
non-flat FLRW backgrounds: McVittie spacetimes embed the vacuum Schwarzschild(-(anti) de Sitter)
spacetime in an isotropic FLRW background universe. We study the global
structure of McVittie spacetimes with spatially non-flat FLRW backgrounds. This
requires the extension of the definition of such spacetimes, previously given
only for the flat and open cases, to the closed case. We revisit this
definition and show how it gives rise to a unique spacetime (given the FLRW
background, the mass parameter $M$ and the cosmological constant $\Lambda$) in
the open and flat cases. In the closed case, an additional free function of the
cosmic time arises. We derive some basic results on the metric, curvature and
matter content of McVittie spacetimes and derive a representation of the line
element that makes the study of their global properties possible. In the closed
case (independently of the free function mentioned above), the spacetime is
confined (at each instant of time) to a region bounded by a minimum and a
maximum area radius, and is bounded either to the future or to the past by a
scalar curvature singularity. This allowed region only exists when the
background scale factor is above a certain minimum. In the open case, radial
null geodesics originate in finite affine time in the past at a boundary formed
by the union of the Big Bang singularity of the FLRW background and a
non-singular hypersurface of varying causal character. Furthermore, in the case
of eternally expanding open universes, we show that black holes are ubiquitous:
ingoing radial null geodesics extend in finite affine time to a hypersurface
that forms the boundary of the region from which photons can escape to future
null infinity. We revisit the black hole interpretation of McVittie spacetimes
in the spatially flat case, and show that this interpretation holds also in the
case of a vanishing cosmological constant, contrary to a previous claim of
ours. | gr-qc |
Relaxations of perturbations of spacetimes in general relativity coupled
to nonlinear electrodynamics: Three well known exact regular solutions of general relativity (GR) coupled
to nonlinear electrodynamics (NED), namely the Maxwellian, Bardeen and Hayward
regular spacetimes, which can describe either a regular black hole or a
geometry without horizons, have been considered. Relaxation times for the
scalar, electromagnetic (EM) and gravitational perturbations of black holes
(BHs) and no-horizon spacetimes have been estimated in comparison with the ones
of the Schwarzschild and Reissner-Nordstr\"{o}m (RN) spacetimes. It has been
shown that the considered geometries in GR coupled to the NED have never
vanishing circular photon orbits and on account of this fact these spacetimes
always oscillate the EM perturbations with quasinormal frequencies (QNFs).
Moreover we have shown that the EM perturbations in the eikonal regime can be a
powerful tool to confirm that (i) the light rays do not follow null geodesics
in the NED by the relaxation rates; (ii) if the underlying solution has a
correct weak field limit to the Maxwell electrodynamics (LED) by the angular
velocity of the circular photon orbit. | gr-qc |
Euclidean Maxwell Theory in the Presence of Boundaries: This paper describes recent progress in the analysis of relativistic gauge
conditions for Euclidean Maxwell theory in the presence of boundaries. The
corresponding quantum amplitudes are studied by using Faddeev-Popov formalism
and zeta-function regularization, after expanding the electromagnetic potential
in harmonics on the boundary 3-geometry. This leads to a semiclassical analysis
of quantum amplitudes, involving transverse modes, ghost modes, coupled normal
and longitudinal modes, and the decoupled normal mode of Maxwell theory. On
imposing magnetic or electric boundary conditions, flat Euclidean space bounded
by two concentric 3-spheres is found to give rise to gauge-invariant one-loop
amplitudes, at least in the cases considered so far. However, when flat
Euclidean 4-space is bounded by only one 3-sphere, one-loop amplitudes are
gauge-dependent, and the agreement with the covariant formalism is only
achieved on studying the Lorentz gauge. Moreover, the effects of gauge modes
and ghost modes do not cancel each other exactly for problems with boundaries.
Remarkably, when combined with the contribution of physical (i.e. transverse)
degrees of freedom, this lack of cancellation is exactly what one needs to
achieve agreement with the results of the Schwinger-DeWitt technique. The most
general form of coupled eigenvalue equations resulting from arbitrary
gauge-averaging functions is now under investigation. | gr-qc |
Fundamental Symmetries of the extended Spacetime: On the basis of Fourier duality and Stone-von Neumann theorem, we will
examine polymer-quantization techniques and modified uncertainty relations as
possible 1-extraD compactification schemes for a phenomenological truncation of
the extraD tower. | gr-qc |
A tight constraint on some varying speed of light theories: We argue that if the velocity of electromagnetic waves in vacuum, \cem, is
different from the limiting velocity for massive particles, \cst, then, a
proton moving with velocity $\cem < v < \cst$ would radiate Cherenkov
radiation. Because we have seen protons with energy $\sim 10^{19}$ eV coming
from a distance of order more than 1 Mpc, we can put a constraint on $\Delta :=
(\cst - \cem)/\cst$: $\Delta < 10^{-27}$. | gr-qc |
Consistency of the nonflat $Λ$CDM model with the new result from
BOSS: Using 137,562 quasars in the redshift range $2.1\leq z\leq3.5$ from the Data
Release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of
Sloan Digital Sky Survey (SDSS)-III, the BOSS-SDSS collaboration estimated the
expansion rate $H(z=2.34)=222\pm7$ km/s/Mpc of Universe, and reported that this
value is in tension with the predictions of flat $\Lambda$CDM model at around
2.5$\sigma$ level. In this paper, we briefly describe some attempts made in the
literature to relieve the tension, and show that the tension can naturally be
alleviated in non-flat $\Lambda$CDM model with positive curvature. We also
perform the observational consistency check by considering the constraints on
the non-flat $\Lambda$CDM model from Planck,WP and BAO data. We find that the
non-flat $\Lambda$CDM model constrained with Planck+WP data fits better to the
line of sight measurement $H(z=2.34)=222\pm7$ km/s/Mpc, but only at the expense
of still having a poor fit to the BAO transverse measurements. | gr-qc |
Semiclassical states in quantum gravity: Curvature associated to a
Voronoi graph: The building blocks of a quantum theory of general relativity are expected to
be discrete structures. Loop quantum gravity is formulated using a basis of
spin networks (wave functions over oriented graphs with coloured edges), thus
realizing the aforementioned expectation. Semiclassical states should, however,
reproduce the classical smooth geometry in the appropriate limits. The question
of how to recover a continuous geometry from these discrete structures is,
therefore, relevant in this context. Following previous works by Bombelli et
al. we explore this problem from a rather general mathematical perspective
using, in particular, properties of Voronoi graphs to search for their
compatible continuous geometries. We test the previously proposed methods for
computing the curvature associated to such graphs and analyse the framework in
detail, in the light of the results obtained. | gr-qc |
Quantum Lightcone Fluctuations in Compactified Spacetimes: We treat the effects of compactified spatial dimensions on the propagation of
light in the uncompactified directions in the context of linearized quantum
gravity. We find that the flight times of pulses can fluctuate due to
modification of the graviton vacuum by the compactification. In the case of a
five dimensional Kaluza-Klein theory, the mean variation in flight time can
grow logarithmically with the flight distance. This effect is in principle
observable, but too small to serve as a realistic probe of the existence of
extra dimensions. We also examine the effect of the compactification on the
widths of spectral lines, and find that there is a small line narrowing effect.
This effect is also small for compactification well above the Planck scale, but
might serve as a test of the existence of extra dimensions. | gr-qc |
Approximate Noether Symmetries of the Geodesic Equations for the
Charged-Kerr Spacetime and Rescaling of Energy: Using approximate symmetry methods for differential equations we have
investigated the exact and approximate symmetries of a Lagrangian for the
geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the
exact case, it is shown that the symmetry algebra of the Lagrangian is 17
dimensional. This algebra is related to the 15 dimensional Lie algebra of
conformal isometries of Minkowski spacetime. First introducing spin angular
momentum per unit mass as a small parameter we consider first-order approximate
symmetries of the Kerr metric as a first perturbation of the Schwarzschild
metric. We then consider the second-order approximate symmetries of the Kerr
metric as a second perturbation of the Minkowski metric. The approximate
symmetries are recovered for these spacetimes and there are no non-trivial
approximate symmetries. A rescaling of the arc length parameter for consistency
of the trivial second-order approximate symmetries of the geodesic equations
indicates that the energy in the charged-Kerr metric has to be rescaled and the
rescaling factor is $r$-dependent. This rescaling factor is compared with that
for the Reissner-Nordstr\"{o}m metric. | gr-qc |
The initial value problem for linearized gravitational perturbations of
the Schwarzschild naked singularity: The coupled equations for the scalar modes of the linearized Einstein
equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1
wave equation with a potential $V$, on a field $\Psi_z$. For smooth metric
perturbations $\Psi_z$ is singular at $r_s=-6M/(\ell-1)(\ell+2)$, $\ell$ the
mode harmonic number, and $V$ has a second order pole at $r_s$. This is
irrelevant to the black hole exterior stability problem, where $r>2M>0$, and
$r_s <0$, but it introduces a non trivial problem in the naked singular case
where $M<0$, then $r_s>0$, and the singularity appears in the relevant range of
$r$. We solve this problem by developing a new approach to the evolution of the
even mode, based on a {\em new gauge invariant function}, $\hat \Psi$ -related
to $\Psi_z$ by an intertwiner operator- that is a regular function of the
metric perturbation {\em for any value of $M$}. This allows to address the
issue of evolution of gravitational perturbations in this non globally
hyperbolic background, and to complete the proof of the linear instability of
the Schwarzschild naked singularity, by showing that a previously found
unstable mode is excitable by generic initial data. This is further illustrated
by numerically solving the linearized equations for suitably chosen initial
data. | gr-qc |
Partition Function of the Schwarzschild Black Hole: We consider a microscopic model of a stretched horizon of the Schwarzschild
black hole. In our model the stretched horizon consists of a finite number of
discrete constituents. Assuming that the quantum states of the Schwarzschild
black hole are encoded in the quantum states of the constituents of its
stretched horizon in a certain manner we obtain an explicit, analytic
expression for the partition function of the hole. Our partition function
predicts, among other things, the Hawking effect, and provides it with a
microscopic, statistical interpretation. | gr-qc |
The singular field used to calculate the self-force on non-spinning and
spinning particles: The singular field of a point charge has recently been described in terms of
a new Green's function of curved spacetime. This singular field plays an
important role in the calculation of the self-force acting upon the particle.
We provide a method for calculating the singular field and a catalog of
expansions of the singular field associated with the geodesic motion of
monopole and dipole sources for scalar, electromagnetic and gravitational
fields. These results can be used, for example, to calculate the effects of the
self-force acting on a particle as it moves through spacetime. | gr-qc |
Gravitational waves and stability of cosmological solutions in the
theory with anomaly-induced corrections: The dynamics of metric perturbations is explored in the gravity theory with
anomaly-induced quantum corrections. Our first purpose is to derive the
equation for gravitational waves in this theory on the general homogeneous and
isotropic background, and then verify the stability of such background with
respect to metric perturbations. The problem under consideration has several
interesting applications. Our first purpose is to explore the stability of the
classical cosmological solutions in the theory with quantum effects taken into
account. There is an interesting literature about stability of Minkowski and de
Sitter spaces and here we extend the consideration also to the radiation and
matter dominated cosmologies. Furthermore, we analyze the behavior of metric
perturbations during inflationary period, in the stable phase of the Modified
Starobinsky inflation. | gr-qc |
Random projections in gravitational-wave searches from compact binaries
II: efficient reconstruction of the detection statistic: Low-latency gravitational wave search pipelines such as GstLAL take advantage
of low-rank factorization of the template matrix via singular value
decomposition (SVD). With unprecedented improvements in detector bandwidth and
sensitivity in advanced-LIGO and Virgo detectors, one expects several orders of
magnitude increase in the size of template banks. This poses a formidable
computational challenge in factorizing huge template matrices. Previously, [in
Kulkarni et al. [6]], we introduced the idea of random projection (RP)-based
matrix factorization as a computationally viable alternative to SVD, applicable
for large template banks. This follow-up paper demonstrates the application of
a block-wise randomized matrix factorization (RMF) algorithm for computing
low-rank factorizations at a preset average fractional loss of SNR. This new
scheme is shown to be more efficient in the context of the LLOID framework of
the GstLAL search pipeline. Further, it is well-known that for huge template
banks, the total computational cost of the search is dominated by
reconstructing the detection statistic compared to that of filtering the data.
However, optimizing the reconstruction cost has not been addressed
satisfactorily so far in the available literature. We show that it is possible
to approximately reconstruct the time-series of the matched-filter detection
statistic at a fraction of the total cost using the matching pursuit algorithm.
Combining the two algorithms presented in this paper can handle online searches
involving large template banks more efficiently. We have analyzed the total
computational cost in detail and offer various tips for optimally applying the
RMF scheme in different parts of the parameter space. The algorithms presented
in this paper are designed in a suitable manner that can be efficiently
implemented over a distributed computing architecture. | gr-qc |
Volume average regularization for the Wheeler-DeWitt equation: In this article, I present a volume average regularization for the second
functional derivative operator that appears in the metric-basis Wheeler-DeWitt
equation. Naively, the second functional derivative operator in the
Wheeler-DeWitt equation is infinite, since it contains terms with a factor of a
delta function or derivatives of the delta function. More precisely, the second
functional derivative contains terms that are only well defined as a
distribution---these terms only yield meaningful results when they appear
within an integral. The second functional derivative may, therefore, be
regularized by performing an integral average of the distributional terms over
some finite volume; I argue that such a regularization is appropriate if one
regards quantum general relativity (from which the Wheeler-DeWitt equation may
be derived) to be the low-energy effective field theory of a full theory of
quantum gravity. I also show that a volume average regularization can be viewed
as a natural generalization of the same-variable second partial derivative for
an ordinary multivariable function. Using the regularized second functional
derivative operator, I construct an approximate solution to the Wheeler-DeWitt
equation in the low-curvature, long-distance limit. | gr-qc |
Probing Accretion Physics with Gravitational Waves: Gravitational-wave observations of extreme mass ratio inspirals (EMRIs) offer
the opportunity to probe the environments of active galactic nuclei (AGN)
through the torques that accretion disks induce on the binary. Within a
Bayesian framework, we study how well such environmental effects can be
measured using gravitational wave observations from the Laser Interferometer
Space Antenna (LISA). We focus on the torque induced by planetary-type
migration on quasicircular inspirals, and use different prescriptions for
geometrically thin and radiatively efficient disks. We find that LISA could
detect migration for a wide range of disk viscosities and accretion rates, for
both $\alpha$ and $\beta$ disk prescriptions. For a typical EMRI with masses
$50M_\odot+10^6M_\odot$, we find that LISA could distinguish between migration
in $\alpha$ and $\beta$ disks and measure the torque amplitude with $\sim 20\%$
relative precision. Provided an accurate torque model, we also show how to turn
gravitational-wave measurements of the torque into constraints on the disk
properties. Furthermore, we show that, if an electromagnetic counterpart is
identified, the multimessenger observations of the AGN EMRI system will yield
direct measurements of the disk viscosity. Finally, we investigate the impact
of neglecting environmental effects in the analysis of the gravitational-wave
signal, finding 3$\sigma$ biases in the primary mass and spin, and showing that
ignoring such effects can lead to false detection of a deviation from general
relativity. This work demonstrates the scientific potential of gravitational
observations as probes of accretion-disk physics, accessible so far through
electromagnetic observations only. | gr-qc |
Nonlinear and Perturbative Evolution of Distorted Black Holes. II.
Odd-parity Modes: We compare the fully nonlinear and perturbative evolution of nonrotating
black holes with odd-parity distortions utilizing the perturbative results to
interpret the nonlinear results. This introduction of the second polarization
(odd-parity) mode of the system, and the systematic use of combined techniques
brings us closer to the goal of studying more complicated systems like
distorted, rotating black holes, such as those formed in the final inspiral
stage of two black holes. The nonlinear evolutions are performed with the 3D
parallel code for Numerical Relativity, {Cactus}, and an independent
axisymmetric code, {Magor}. The linearized calculation is performed in two
ways: (a) We treat the system as a metric perturbation on Schwarzschild, using
the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the
system as a curvature perturbation of a Kerr black hole (but here restricted to
the case of vanishing rotation parameter a) and evolve it with the Teukolsky
equation The comparisons of the waveforms obtained show an excellent agreement
in all cases. | gr-qc |
Black hole thermodynamics from logotropic fluids: We show that the Einstein field equations with a negative cosmological
constant can admit black hole solutions whose thermodynamics coincides with
that of logotropic fluids, recently investigated to heal some cosmological and
astrophysical issues. For this purpose, we adopt the Anton-Schmidt equation of
state, which represents a generalized version of logotropic fluids. We thus
propose a general treatment to obtain an asymptotic anti-de Sitter metric,
reproducing the thermodynamic properties of both Anton-Schmidt and logotropic
fluids. Hence, we explore how to construct suitable spacetime functions,
invoking an event horizon and fulfilling the null, weak, strong and dominant
energy conditions. We further relax the strong energy condition to search for
possible additional solutions. Finally, we discuss the optical properties
related to a specific class of metrics and show how to construct an effective
refractive index depending on the spacetime functions and the thermodynamic
quantities of the fluid under study. We also explore possible departures with
respect to the case without the fluid. | gr-qc |
Tidal heating as a discriminator for horizons in extreme mass ratio
inspirals: The defining feature of a classical black hole is being a perfect absorber.
Any evidence showing otherwise would indicate a departure from the standard
black-hole picture. Energy and angular momentum absorption by the horizon of a
black hole is responsible for tidal heating in a binary. This effect is
particularly important in the latest stages of an extreme mass ratio inspiral
around a spinning supermassive object, one of the main targets of the future
LISA mission. We study how this effect can be used to probe the nature of
supermassive objects in a model independent way. We compute the orbital
dephasing and the gravitational-wave signal emitted by a point particle in
circular, equatorial motion around a spinning supermassive object to the
leading order in the mass ratio. Absence of absorption by the central object
can affect the gravitational-wave signal dramatically, especially at high spin.
This effect will make it possible to put an unparalleled upper bound on the
reflectivity of exotic compact objects, at the level of ${\cal O}(0.01)\%$.
This stringent bound would exclude the possibility of observing echoes in the
ringdown of a supermassive binary merger. | gr-qc |
Exploring the self-tuning of the cosmological constant from Planck mass
variation: Recently, the variation of the Planck mass in the General Relativistic
Einstein-Hilbert action was proposed as a self-tuning mechanism of the
cosmological constant, preventing Standard Model vacuum energy from freely
gravitating and enabling an estimation of the magnitude of its observed value.
We explore here new aspects of this proposal. We first develop an equivalent
Einstein-frame formalism to the current Jordan-frame formulation of the
mechanism and use this to highlight similarities and differences of self-tuning
to the sequestering mechanism. We then show how with an extension of the local
self-tuning action by a coupled Gauss-Bonnet term and a companion four-form
field strength, graviton loops can be prevented from incapacitating the
degravitation of the Standard Model vacuum energy. For certain cases, we
furthermore find that this extension can be recast as a Horndeski scalar-tensor
theory and be embedded in the conventional local self-tuning formalism. We then
explore the possibility of a unification of inflation with self-tuning. The
resulting equations can alternatively be used to motivate a multiverse
interpretation. In this context, we revisit the coincidence problem and provide
an estimation for the probability of the emergence of intelligent life in our
Universe as a function of cosmic age, inferred from star and terrestrial planet
formation processes. We conclude that we live at a very typical epoch, where we
should expect the energy densities of the cosmological constant and matter to
be of comparable size. For a dimensionless quantity to compare the emergence of
life throughout the cosmic history of different universes in an anthropic
analysis of the multiverse, we choose the order of magnitude difference of the
evolving horizon size of a universe to the size of its proton as the basic
building block of atoms, molecules, and eventually life. (abridged) | gr-qc |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.