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Quest for realistic non-singular black-hole geometries: Regular-center
type: We propose seven criteria to single out physically reasonable non-singular
black-hole models and adopt them to four different spherically symmetric models
with a regular center and their rotating counterparts. In general relativity,
all such non-singular black holes are non-generic with a certain matter field
including a class of nonlinear electromagnetic fields. According to a criterion
that the effective energy-momentum tensor should satisfy all the standard
energy conditions in asymptotically flat regions, the well-known Bardeen and
Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang
black holes respect the dominant energy condition everywhere. Although the
rotating Fan-Wang black hole contains a curvature singularity, the rotating
Dymnikova black hole is free from scalar polynomial curvature singularities and
closed timelike curves. In addition, the dominant energy condition is respected
on and outside the event horizons in the latter case. The absence of parallelly
propagated curvature singularities remains an open question. | gr-qc |
Entanglement harvesting between two inertial Unruh-DeWitt detectors from
non-vacuum quantum fluctuations: Entanglement harvesting from the quantum field is a well-known fact that, in
recent times, is being rigorously investigated further in flat and different
curved backgrounds. The usually understood formulation studies the possibility
of two uncorrelated Unruh-DeWitt detectors getting entangled over time due to
the effects of quantum vacuum fluctuations. Our current work presents a
thorough formulation to realize the entanglement harvesting from non-vacuum
background fluctuations. In particular, we further consider single excitation
field states and a pair of inertial detectors, respectively, in $(1+1)$ and
$(1+3)$ dimensions for this investigation. Our main observation asserts that
entanglement harvesting is suppressed compared to the vacuum fluctuations in
this situation. Our other observations confirm a non-zero individual detector
transition probability in this background and vanishing entanglement harvesting
for parallel co-moving detectors. We look into the characteristics of the
harvested entanglement and discuss its dependence on different system
parameters. | gr-qc |
Noether Symmetries and Some Exact Solutions in $f(R, T^{2})$ Theory: The main objective of this article is to examine some physically viable
solutions through the Noether symmetry technique in $f(R, T^{2})$ theory. For
this purpose, we assume a generalized anisotropic and homogenous spacetime that
yields distinct cosmic models. In order to investigate Noether equations,
symmetry generators and conserved quantities, we use a specific model of this
modified theory. We find exact solutions and examine the behavior of various
cosmological quantities. It is found the behavior these quantities is
consistent with current observations indicating that this theory describes the
cosmic accelerated expansion. We conclude that generators of Noether symmetry
and conserved quantities exist in this theory. | gr-qc |
Electromagnetic duality anomaly in curved spacetimes: The source-free Maxwell action is invariant under electric-magnetic duality
rotations in arbitrary spacetimes. This leads to a conserved classical Noether
charge. We show that this conservation law is broken at the quantum level in
presence of a background classical gravitational field with a non-trivial
Chern-Pontryagin invariant, in a parallel way to the chiral anomaly for
massless Dirac fermions. Among the physical consequences, the net polarization
of the quantum electromagnetic field is not conserved. | gr-qc |
An area rescaling ansatz and black hole entropy from loop quantum
gravity: Considering the possibility of `renormalization' of the gravitational
constant on the horizon, leading to a dependence on the level of the associated
Chern-Simons theory, a rescaled area spectrum is proposed for the non-rotating
black hole horizon in loop quantum gravity. The statistical mechanical
calculation leading to the entropy provides a unique choice of the rescaling
function for which the Bekenstein-Hawking area law is yielded without the need
to choose the Barbero-Immirzi parameter $(\gamma)$. $\gamma$ is determined by
studying the limit in which the `renormalized' gravitational constant on the
horizon asymptotically approaches the `bare' value. Unlike the usual, much
criticized, practice of choosing $\gamma$ just for the sake of the entropy
matching the area law, its value is now rather determined by a physical
consistency requirement. | gr-qc |
Friedmann Robertson-Walker model in generalised metric space-time with
weak anisotropy: A generalized model of space-time is given, taking into consideration the
anisotropic structure of fields which are depended on the position and the
direction (velocity).In this framework a generalized FRW-metric the
Raychaudhouri and Friedmann equations are studied.A long range vector field of
cosmological origin is considered in relation to the physical geometry of
space-time in which Cartan connection has a fundamental role.The generalised
Friedmann equations are produced including anisotropic terms.The variation of
anisotropy $z_t$ is expressed in terms of the Cartan torsion tensor of the
Finslerian space-time.A possible estimation of the anisotropic parameter $z_t$
can be achieved with the aid of the de-Sitter model of the empty flat universe
with weak anisotropy. Finally a physical generalisation for the model of
inflation is also studied. | gr-qc |
Solving the Initial Value Problem of two Black Holes: We solve the elliptic equations associated with the Hamiltonian and momentum
constraints, corresponding to a system composed of two black holes with
arbitrary linear and angular momentum. These new solutions are based on a
Kerr-Schild spacetime slicing which provides more physically realistic
solutions than the initial data based on conformally flat metric/maximal
slicing methods. The singularity/inner boundary problems are circumvented by a
new technique that allows the use of an elliptic solver on a Cartesian grid
where no points are excised, simplifying enormously the numerical problem. | gr-qc |
Holographic reconstruction of $f(G)$ Gravity for scale factors
pertaining to Emergent, Logamediate and Intermediate scenarios: In this paper, we reconstruct the holographic dark energy in the framework of
$f(G)$ modified theory of gravity, where $G$ is Gauss-Bonnet invariant. In this
context, we choose the infrared cut-off as Granda-Oliveros cut-off which is
proportional to the Hubble parameter $H$ and its first derivative with respect
to the cosmic time $t$. We reconstruct $f(G)$ model with the inclusion of HDE
and three well-known forms of the scale factor $a(t)$, i.e. the emergent, the
logamediate and the intermediate scale factors. The reconstructed model as well
as equation of state parameter are discussed numerically with the help of
graphical representation to explore the accelerated expansion of the universe.
Moreover, the stability of the models incorporating all the scale factors is
checked through squared speed of sound $v_s^2$. | gr-qc |
Vacuum Static Spherically Symmetric Spacetimes in Harada's Theory: Very recently Harada proposed a gravitational theory which is of third order
in the derivatives of the metric tensor with the property that any solution of
Einstein's field equations (EFEs) possibly with a cosmological constant is
necessarily a solution of the new theory. He then applied his theory to derive
a second-order ODE for the evolution of the scale factor of the FLRW metric.
Remarkably he showed that, even in a matter-dominated universe with zero
cosmological constant, there is a late-time transition from decelerating to
accelerating expansion. Harada also derived a generalisation of the
Schwarzschild solution. However, as his starting point he assumed an
unnecessarily restricted form for a static spherically symmetric metric. In
this note the most general spherically symmetric static vacuum solution of the
theory is derived.
Mantica and Molinari have shown that Harada's theory may be recast into the
form of the EFEs with an additional source term in the form of a second-order
conformal Killing tensor(CKT). Accordingly they have dubbed the theory
conformal Killing gravity. Then, using a result in a previous paper of theirs
on CKTs in generalised Robertson-Walker spacetimes, they rederived Harada's
generalised evolution equation for the scale factor of the FLRW metric.
However, Mantica and Molinari appear to have overlooked the fact that all
solutions of the new theory (except those satisfying the EFEs) admit a
non-trivial second-order Killing tensor. Such Killing tensors are invaluable
when considering the geodesics of a metric as they lead to a second quadratic
invariant of the motion in addition to that derived from the metric. | gr-qc |
Dressed metric predictions revisited: It was recently shown that the volume operator of loop quantum cosmology
(LQC) and all its positive powers are ill-defined on physical states. In this
paper, we investigate how it effects predictions of cosmic microwave background
(CMB) power spectra obtained within dressed metric approach for which
expectations values of $\hat{a}$ are the key element. We find that almost every
step in the procedure is ill-defined and relies heavily upon a (seemingly
premature) numerical truncation. Thus, it suggests that more care is needed in
making predictions regarding pre-inflationary physics. We propose a new scheme
which contains only well-defined quantities. The surprising agreement of the
hitherto models with observational data, especially at low angular momenta $l$
is explained. | gr-qc |
Families of exact solutions of a 2D gravity model minimally coupled to
electrodynamics: Three families of exact solutions for 2-dimensional gravity minimally coupled
to electrodynamics are obtained in the context of ${\cal R}=T$ theory. It is
shown, by supersymmetric formalism of quantum mechanics, that the quantum
dynamics of a neutral bosonic particle on static backgrounds with both varying
curvature and electric field is exactly solvable. | gr-qc |
Linear stochastic wave-equations for continuously measured quantum
systems: While the linearity of the Schr\"odinger equation and the superposition
principle are fundamental to quantum mechanics, so are the backaction of
measurements and the resulting nonlinearity. It is remarkable, therefore, that
the wave-equation of systems in continuous interaction with some reservoir,
which may be a measuring device, can be cast into a linear form, even after the
degrees of freedom of the reservoir have been eliminated. The superposition
principle still holds for the stochastic wave-function of the observed system,
and exact analytical solutions are possible in sufficiently simple cases. We
discuss here the coupling to Markovian reservoirs appropriate for homodyne,
heterodyne, and photon counting measurements. For these we present a derivation
of the linear stochastic wave-equation from first principles and analyze its
physical content. | gr-qc |
Semiclassical relativistic stars: We present strong evidence that semiclassical gravity can give place to
self-consistent ultracompact stars beyond the Buchdahl limit. We integrate the
semiclassical equations of (spherically symmetric) stellar equilibrium for a
constant-density classical fluid. The semiclassical contribution is modelled by
a quantum massless scalar field in the only static vacuum state compatible with
asymptotic flatness (Boulware vacuum). The Renormalized Stress-Energy Tensor
(RSET) is firstly approximated by the analytic Polyakov approximation. This
already reveals a crucial difference with respect to purely classical
solutions: stars with compactness close to that of a black hole exhibit bounded
pressures and curvatures up to a very small central core compared with the star
radius. This suggests that a more refined approximation to the RSET at the core
may give rise to strictly regular configurations. Following this suggestion, we
prove that a minimal deformation of the Polyakov approximation inside the
central core is sufficient to produce regular ultracompact stellar
configurations. | gr-qc |
Dilatonic Entropic Force: We show in detail that the entropic force of the static spherically symmetric
spacetimes with unusual asymptotics can be calculated through the Verlinde's
arguments. We introduce three different holographic screen candidates, which
are first employed thoroughly by Myung and Kim [Phys. Rev. D 81, 105012 (2010)]
for Schwarzschild black hole solutions, in order to identify the entropic force
arising between a charged dilaton black hole and a test particle. The
significance of the dilaton parameter on the entropic force is highlighted, and
shown graphically. | gr-qc |
Precision tests of General Relativity with Matter Waves: We review the physics of atoms and clocks in weakly curved spacetime, and how
each may be used to test the Einstein Equivalence Principle (EEP) in the
context of the minimal Standard Model Extension (mSME). We find that
conventional clocks and matter-wave interferometers are sensitive to the same
kinds of EEP-violating physics. We show that the analogy between matter-waves
and clocks remains true for systems beyond the semiclassical limit. We
quantitatively compare the experimentally observable signals for EEP violation
in matter-wave experiments. We find that comparisons of $^{6}$Li and $^{7}$Li
are particularly sensitive to such anomalies. Tests involving unstable
isotopes, for which matter-wave interferometers are well suited, may further
improve the sensitivity of EEP tests. | gr-qc |
Second post-Newtonian order radiative dynamics of inspiralling compact
binaries in the Effective Field Theory approach: We use the Effective Field Theory (EFT) framework to compute the mass
quadrupole moment, the equation of motion, and the power loss of inspiralling
compact binaries at the second order in the Post-Newtonian (PN) approximation.
We present expressions for the stress-energy pseudo-tensor components of the
binary system in higher PN orders. The 2PN correction to the mass quadrupole
moment as well as to the acceleration computed in the linearized harmonic gauge
presented here are the ingredients needed for the calculation of the
next-to-next-to leading order radiation reaction force, which will be presented
elsewhere. While this paper reproduces known results, it supplies the building
blocks necessary for future higher order calculations in the EFT methodology. | gr-qc |
Measuring Gravito-magnetic Effects by Multi Ring-Laser Gyroscope: We propose an under-ground experiment to detect the general relativistic
effects due to the curvature of space-time around the Earth (de Sitter effect)
and to rotation of the planet (dragging of the inertial frames or
Lense-Thirring effect). It is based on the comparison between the IERS value of
the Earth rotation vector and corresponding measurements obtained by a
tri-axial laser detector of rotation. The proposed detector consists of six
large ring-lasers arranged along three orthogonal axes.
In about two years of data taking, the 1% sensitivity required for the
measurement of the Lense-Thirring drag can be reached with square rings of 6
$m$ side, assuming a shot noise limited sensitivity ($ 20 prad/s/\sqrt{Hz}$).
The multi-gyros system, composed of rings whose planes are perpendicular to one
or the other of three orthogonal axes, can be built in several ways. Here, we
consider cubic and octahedron structures. The symmetries of the proposed
configurations provide mathematical relations that can be used to study the
stability of the scale factors, the relative orientations or the ring-laser
planes, very important to get rid of systematics in long-term measurements,
which are required in order to determine the relativistic effects. | gr-qc |
Electromagnetic quasinormal modes of D-dimensional black holes II: By using the sixth order WKB approximation we calculate for an
electromagnetic field propagating in D-dimensional Schwarzschild and
Schwarzschild de Sitter black holes its quasinormal frequencies for the
fundamental mode and first overtones. We study the dependence of these QN
frequencies on the value of the cosmological constant and the spacetime
dimension. We also compare with the known results for the gravitational
perturbations propagating in the same background. Moreover we exactly compute
the QN frequencies of the electromagnetic field propagating in D-dimensional
massless topological black hole and for charged D-dimensional Nariai spacetime
we exactly calculate the QN frequencies of the coupled electromagnetic and
gravitational perturbations. | gr-qc |
Learning about Quantum Gravity with a Couple of Nodes: Loop Quantum Gravity provides a natural truncation of the infinite degrees of
freedom of gravity, obtained by studying the theory on a given finite graph. We
review this procedure and we present the construction of the canonical theory
on a simple graph, formed by only two nodes. We review the U(N) framework,
which provides a powerful tool for the canonical study of this model, and a
formulation of the system based on spinors. We consider also the covariant
theory, which permits to derive the model from a more complex formulation,
paying special attention to the cosmological interpretation of the theory. | gr-qc |
A light-cone gauge for black-hole perturbation theory: The geometrical meaning of the Eddington-Finkelstein coordinates of
Schwarzschild spacetime is well understood: (i) the advanced-time coordinate v
is constant on incoming light cones that converge toward r=0, (ii) the angles
theta and phi are constant on the null generators of each light cone, (iii) the
radial coordinate r is an affine-parameter distance along each generator, and
(iv) r is an areal radius, in the sense that 4 pi r^2 is the area of each
two-surface (v,r) = constant. The light-cone gauge of black-hole perturbation
theory, which is formulated in this paper, places conditions on a perturbation
of the Schwarzschild metric that ensure that properties (i)--(iii) of the
coordinates are preserved in the perturbed spacetime. Property (iv) is lost in
general, but it is retained in exceptional situations that are identified in
this paper. Unlike other popular choices of gauge, the light-cone gauge
produces a perturbed metric that is expressed in a meaningful coordinate
system; this is a considerable asset that greatly facilitates the task of
extracting physical consequences. We illustrate the use of the light-cone gauge
by calculating the metric of a black hole immersed in a uniform magnetic field.
We construct a three-parameter family of solutions to the perturbative
Einstein-Maxwell equations and argue that it is applicable to a broader range
of physical situations than the exact, two-parameter Schwarzschild-Melvin
family. | gr-qc |
The twin paradox: the role of acceleration: The twin paradox, which evokes from the the idea that two twins may age
differently because of their relative motion, has been studied and explained
ever since it was first described in 1906, the year after special relativity
was invented. The question can be asked: "Is there anything more to say?" It
seems evident that acceleration has a role to play, however this role has
largely been brushed aside since it is not required in calculating, in a
preferred reference frame, the relative age difference of the twins. Indeed, if
one tries to calculate the age difference from the point of the view of the
twin that undergoes the acceleration, then the role of the acceleration is
crucial and cannot be dismissed. In the resolution of the twin paradox, the
role of the acceleration has been denigrated to the extent that it has been
treated as a red-herring. This is a mistake and shows a clear misunderstanding
of the twin paradox. | gr-qc |
Efficient resummation of high post-Newtonian contributions to the
binding energy: A factorisation property of Feynman diagrams in the context the Effective
Field Theory approach to the compact binary problem has been recently employed
to efficiently determine the static sector of the potential at fifth
post-Newtonian (5PN) order. We extend this procedure to the case of non-static
diagrams and we use it to fix, by means of elementary algebraic manipulations,
the value of more than one thousand diagrams at 5PN order, that is a
substantial fraction of the diagrams needed to fully determine the dynamics at
5PN. This procedure addresses the redundancy problem that plagues the
computation of the binding energy with respect to more "efficient" observables
like the scattering angle, thus making the EFT approach in harmonic gauge at
least as scalable as the others methods. | gr-qc |
The Raychaudhuri equation for a quantized timelike geodesic congruence: A recent attempt to arrive at a quantum version of Raychaudhuri's equation is
looked at critically. It is shown that the method, and even the idea, has some
inherent problems. The issues are pointed out here. We have also shown that it
is possible to salvage the method in some limited domain of applicability.
Although no generality can be claimed, a quantum version of the equation should
be useful in the context of ascertaining the existence of a singularity in the
quantum regime. The equation presented in the present work holds for arbitrary
$n + 1$ dimensions. An important feature of the Hamiltonian in the operator
form is that it admits a self-adjoint extension quite generally. Thus, the
conservation of probability is ensured. | gr-qc |
Homoclinic Orbits around Spinning Black Holes II: The Phase Space
Portrait: In paper I in this series, we found exact expressions for the equatorial
homoclinic orbits: the separatrix between bound and plunging, whirling and not
whirling. As a companion to that physical space study, in this paper we paint a
phase space portrait of the homoclinic orbits that includes exact expressions
for the actions and fundamental frequencies. Additionally, we develop a reduced
Hamiltonian description of Kerr motion that allows us to track groups of
trajectories with a single global clock. This facilitates a variational
analysis, whose stability exponents and eigenvectors could potentially be
useful for future studies of families of black hole orbits and their associated
gravitational waveforms. | gr-qc |
Entropy and Area of Black Holes in Loop Quantum Gravity: Simple arguments related to the entropy of black holes strongly constrain the
spectrum of the area operator for a Schwarzschild black hole in loop quantum
gravity. In particular, this spectrum is fixed completely by the assumption
that the black hole entropy is maximum. Within the approach discussed, one
arrives in loop quantum gravity at a quantization rule with integer quantum
numbers $n$ for the entropy and area of a black hole. | gr-qc |
Characteristic initial value problems for integrable hyperbolic
reductions of Einstein's equations: A unified general approach is presented for construction of solutions of the
characteristic initial value problems for various integrable hyperbolic
reductions of Einstein's equations for space-times with two commuting
isometries in General Relativity and in some string theory induced gravity
models. In all cases the associated linear systems of similar structures are
used, and their fundamental solutions admit an alternative representations by
two ``scattering'' matrices of a simple analytical structures on the spectral
plane. The condition of equivalence of these representations leads to the
linear ``integral evolution equations'' whose scalar kernels and right hand
sides are determined completely by the initial data for the fields specified on
the two initial characteristics. If the initial data for the fields are given,
all field components of the corresponding solution can be expressed in
quadratures in terms of a unique solution of these quasi - Fredholm integral
evolution equations. | gr-qc |
Magnetized hairy black holes of dimensionally continued gravity coupled
to double-logarithmic electrodynamics: A recently proposed model for nonlinear electrodynamics has been minimally
coupled to dimensionally continued gravity and the topological black holes in
the presence of conformal scalar field were studied. In this setup, the new
magnetized hairy black hole solution has been found and its thermodynamic
properties have also been analyzed. The exact expressions for mass, entropy,
Hawking temperature and heat capacity are derived and local thermodynamic
stability for the resulting black holes has been checked. In addition to this,
the modified Smarr's formula is constructed and the generalized first law has
also been verified. Finally, the hairy magnetized black holes in general
Lovelock-scalar gravity have also been studied. | gr-qc |
Gravitational Radiation from Cylindrical Naked Singularity: We construct an approximate solution which describes the gravitational
emission from a naked singularity formed by the gravitational collapse of a
cylindrical thick shell composed of dust. The assumed situation is that the
collapsing speed of the dust is very large. In this situation, the metric
variables are obtained approximately by a kind of linear perturbation analysis
in the background Morgan solution which describes the motion of cylindrical
null dust. The most important problem in this study is what boundary conditions
for metric and matter variables should be imposed at the naked singularity. We
find a boundary condition that all the metric and matter variables are
everywhere finite at least up to the first order approximation. This implies
that the spacetime singularity formed by this high-speed dust collapse is very
similar to that formed by the null dust and thus the gravitational emission
from a naked singularity formed by the cylindrical dust collapse can be gentle. | gr-qc |
About Lorentz-Møller-Nelson transformation to rigid noninertial frame
of reference: With a special Lorentz-M{\o}ller-Nelson (LMN) transformation found
transformation of velocity from the laboratory system S to an accelerated,
rotating frame of reference s. The physical sense of parameter entering into
the LMN special transformation is established. For small distances, and their
proper smooth motion without jerks suggested the inverse special LMN
transformation. The main consequences of this transformation is considered,
namely, a) the desync in moving frame of reference s of proper clocks of the
pre-synchronized in the laboratory frame S and b) the Lorentz contraction of
proper rulers of frame s in the frame S. The applicability of the inverse LMN
transformation for real frames with maximum rigidity is established. Equations
for the rotation matrix is obtained. It is shown that the intrinsic rotation of
the axes s, considered with respect to S is not rigid. Found the direct and
inverse transformation of affine "angular" velocity in the S to the comoving,
but not rotating frame s. Also shown that for the non-inertial motion of
rigidly rotating frame of reference her the kinematic deformation of
coordinates system is absent in two planes. The application of this
transformation to a rotating rigid body is considered. The matrice and angle of
proper Wigner rotation is calculated. We find differential equations for the
inverse problem of relativistic kinematics, and their decision in the case of
uniformly accelerated motion. The close connection between the proper Thomas
precession and the proper Wigner rotation and their mutual compensation for the
case uniformly accelerated motion has shown. The difference of the uniformly
accelerated motion from the hyperbolic one has been shown. Also, the basic
formulas are expressed in terms of the parameter, which is solution of the
equation for the inverse problem of relativistic kinematics. | gr-qc |
Astrophysically relevant bound trajectories around a Kerr black hole: We derive alternate and new closed-form analytic solutions for the
non-equatorial eccentric bound trajectories, $\{ \phi \left( r, \theta
\right)$, $\ t \left( r, \theta \right),\ r \left( \theta \right) \}$, around a
Kerr black hole by using the transformation $1/r=\mu \left(1+ e \cos \chi
\right)$. The application of the solutions is straightforward and numerically
fast. We obtain and implement translation relations between energy and angular
momentum of the particle, ($E$, $L$), and eccentricity and inverse-latus
rectum, ($e$, $\mu$), for a given spin, $a$, and Carter's constant, $Q$, to
write the trajectory completely in the ($e$, $\mu$, $a$, $Q$) parameter space.
The bound orbit conditions are obtained and implemented to select the allowed
combination of parameters ($e$, $\mu$, $a$, $Q$). We also derive specialized
formulae for spherical and separatrix orbits. A study of the non-equatorial
analog of the previously studied equatorial separatrix orbits is carried out
where a homoclinic orbit asymptotes to an energetically bound spherical orbit.
Such orbits simultaneously represent an eccentric orbit and an unstable
spherical orbit, both of which share the same $E$ and $L$ values. We present
exact expressions for $e$ and $\mu$ as functions of the radius of the
corresponding unstable spherical orbit, $r_s$, $a$, and $Q$, and their
trajectories, for ($Q\neq0$) separatrix orbits; they are shown to reduce to the
equatorial case. These formulae have applications to study the gravitational
waveforms from EMRIs besides relativistic precession and phase space
explorations. We obtain closed-form expressions of the fundamental frequencies
of non-equatorial eccentric trajectories that are equivalent to the previously
obtained quadrature forms and also numerically match with the equivalent
formulae previously derived. We sketch several orbits and discuss their
astrophysical applications. | gr-qc |
Quadrupole formula for Kaluza-Klein modes in the braneworld: The quadrupole formula in four-dimensional Einstein gravity is a useful tool
to describe gravitational wave radiation. We derive the quadrupole formula for
the Kaluza-Klein (KK) modes in the Randall-Sundrum braneworld model. The
quadrupole formula provides transparent representation of the exterior weak
gravitational field induced by localized sources. We find that a general
isolated dynamical source gives rise to the 1/r^2 correction to the leading 1/r
gravitational field. We apply the formula to an evaluation of the effective
energy carried by the KK modes from the viewpoint of an observer on the brane.
Contrary to the ordinary gravitational waves (zero mode), the flux of the
induced KK modes by the non-spherical part of the quadrupole moment vanishes at
infinity and only the spherical part contributes to the flux. Since the effect
of the KK modes appears in the linear order of the metric perturbations, the
effective energy flux observed on the brane is not always positive, but can
become negative depending on the motion of the localized sources. | gr-qc |
Einstein constraints on a characteristic cone: We analyse the Cauchy problem on a characteristic cone, including its vertex,
for the Einstein equations in arbitrary dimensions. We use a wave map gauge,
solve the obtained constraints and show gauge conservation. | gr-qc |
Renormalisation group improvement of scalar field inflation: We study quantum corrections to Friedmann-Robertson-Walker cosmology with a
scalar field under the assumption that the dynamics are subject to
renormalisation group improvement. We use the Bianchi identity to relate the
renormalisation group scale to the scale factor and obtain the improved
cosmological evolution equations. We study the solutions of these equations in
the renormalisation group fixed point regime, obtaining the time-dependence of
the scalar field strength and the Hubble parameter in specific models with
monomial and trinomial quartic scalar field potentials. We find that power-law
inflation can be achieved in the renormalisation group fixed point regime with
the trinomial potential, but not with the monomial one. We study the transition
to the quasi-classical regime, where the quantum corrections to the couplings
become small, and find classical dynamics as an attractor solution for late
times. We show that the solution found in the renormalisation group fixed point
regime is also a cosmological fixed point in the autonomous phase space. We
derive the power spectrum of cosmological perturbations and find that the
scalar power spectrum is exactly scale-invariant and bounded up to arbitrarily
small times, while the tensor perturbations are tilted as appropriate for the
background power-law inflation. We specify conditions for the renormalisation
group fixed point values of the couplings under which the amplitudes of the
cosmological perturbations remain small. | gr-qc |
Group field theory and its cosmology in a matter reference frame: While the equations of general relativity take the same form in any
coordinate system, choosing a suitable set of coordinates is essential in any
practical application. This poses a challenge in background-independent quantum
gravity, where coordinates are not a priori available and need to be
reconstructed from physical degrees of freedom. We review the general idea of
coupling free scalar fields to gravity and using these scalars as a "matter
reference frame." The resulting coordinate system is harmonic, i.e. it
satisfies harmonic (de Donder) gauge. We then show how to introduce such matter
reference frames in the group field theory approach to quantum gravity, where
spacetime is emergent from a "condensate" of fundamental quantum degrees of
freedom of geometry, and how to use matter coordinates to extract physics. We
review recent results in homogeneous and inhomogeneous cosmology, and give a
new application to the case of spherical symmetry. We find tentative evidence
that spherically symmetric group field theory condensates defined in this
setting can reproduce the near-horizon geometry of a Schwarzschild black hole. | gr-qc |
Scalar charge of black holes in Einstein-Maxwell-dilaton theory: We show that the monopole scalar charge of black holes in
Einstein--Maxwell--dilaton theory is proportional to the electric potential at
the event horizon, with a proportionality factor given by (minus) the scalar
coupling constant. We also show that the scalar charge, in the weak electric
charge limit, does not depend on the black hole spin. This result can be very
useful to circumvent spin degeneracy issues when testing the theory against
gravitational waves observations. | gr-qc |
The Cauchy Horizon in Higher-derivative Gravity Theories: A class of exact solutions of the field equations with higher derivative
terms is presented when the matter field is a pressureless null fluid plus a
Maxwellian static electric component. It is found that the stable solutions are
black holes in anti de Sitter background. The issue of the stability of the
Cauchy horizon is discussed. | gr-qc |
General Relativistic Theory of Light Propagation in the Field of
Radiative Gravitational Multipoles: The extremely high precision of current astronomical observations demands a
much better theoretical treatment of relativistic effects in the propagation of
electromagnetic signals through variable gravitational fields of isolated
astronomical systems emitting gravitational waves. This paper presents a
consistent approach giving a complete and exhaustive solution of this problem
in the first post-Minkowskian approximation of general relativity. | gr-qc |
Thermodynamics from field equations for black holes with multiple
horizons: The first law of black hole thermodynamics can be read off from the field
equations at the horizon. Until now, for black holes with multiple horizons the
field equations only at the outer horizon were employed with a particular
constraint. In this paper, however, we suggest that for a black hole with
multiple horizons the field equations at the inner horizon as well as the outer
horizon should be needed in order to obtain the first law of black hole
thermodynamics in general. | gr-qc |
Warm constant-roll inflation in brane-world cosmology: In this article we study a constant-roll inflationary model in the context of
brane-world cosmology caused by a quintessence scalar field for warm inflation
with a constant dissipative parameter Q =$\Gamma$/3H. We determine the
analytical solution for the Friedman equation coupled to the equation of motion
of the scaler field. The evolution of the primordial scalar and tensor
perturbations is also studied using the modified Langevin equation. To check
the viability of the model we use numerical approaches and plot some figures.
Our results for the scalar spectral index and the tensor to scaler ratio show
good consistency with observations. | gr-qc |
Quantum State and Spontaneous Symmetry Breaking in Gravity: A spontaneous symmetry breaking mechanism is used in quantum gravity to
obtain a convergent positive definite density-matrix as the most general
quantum state of Euclidean wormholes | gr-qc |
New self-consistent effective one-body theory for spinless binaries
based on the post-Minkowskian approximation: The effective one-body theories, introduced by Buonanno and Damour, are novel
approaches to constructing a gravitational waveform template. By taking a gauge
in which $\psi_{1}^{B}$ and $\psi_{3}^{B}$ vanish, we find a decoupled equation
with separable variables for $\psi^{B}_{4}$ for gravitational perturbation in
the effective metric obtained in the post-Minkowskian approximation.
Furthermore, we set up a new self-consistent effective one-body theory for
spinless binaries, which can be applicable to any post-Minkowskian orders. This
theory not only releases the assumption that $v/c$ should be a small quantity
but also resolves the contradiction that the Hamiltonian, radiation-reaction
force, and waveform are constructed from different physical models in the
effective one-body theory with the post-Newtonian approximation. Compared with
our previous theory (Science China, 65, 260411, (2022)), the computational
effort for the radiation-reaction force and waveform in this new theory will be
tremendously reduced. | gr-qc |
Model-independent distance calibration of high-redshift gamma-ray bursts
and constrain on the $Λ$CDM model: Gamma-ray bursts (GRBs) are luminous enough to be detectable up to redshift
$z\sim 10$. They are often proposed as complementary tools to type-Ia
supernovae (SNe Ia) in tracing the Hubble diagram of the Universe. The distance
calibrations of GRBs usually make use one or some of the empirical luminosity
correlations, such as $\tau_{\rm lag}-L$, $V-L$, $E_p-L$, $E_p-E_{\gamma}$,
$\tau_{\rm RT}-L$ and $E_p-E_{\rm iso}$ relations. These calibrating methods
are based on the underling assumption that the empirical luminosity
correlations are universal over all redshift range. In this paper, we test the
possible redshift dependence of six luminosity correlations by dividing GRBs
into low-$z$ and high-$z$ classes according to their redshift smaller or larger
than 1.4. It is shown that the $E_p-E_{\gamma}$ relation for low-$z$ GRBs is
consistent with that for high-$z$ GRBs within $1\sigma$ uncertainty. The
intrinsic scatter of $V-L$ relation is too larger to make a convincing
conclusion. For the rest four correlations, however, low-$z$ GRBs differ from
high-$z$ GRBs at more than $3\sigma$ confidence level. As such, we calibrate
GRBs using the $E_p-E_{\gamma}$ relation in a model-independent way. The
constraint of high-$z$ GRBs on the $\Lambda$CDM model gives $\Omega_M=0.302\pm
0.142(1\sigma)$, well consistent with the Planck 2015 results. | gr-qc |
Did the Pseudo-Sphere Universe have a Beginning?: A calculation of the no-boundary wave-function of the universe is put forward
for a spacetime with negative curvature. A semi-classical Robertson-Walker
approximation is attempted and two solutions to the field equations, one
Lorentzian and the other a tunneling one are found. The regularity of those
solutions are analysed explicitly, both in 2+1 and 3+1 dimensions and a conical
singularity is found at the origin of the time axis, contradicting the
no-boundary assumption. | gr-qc |
Quantum Big Bounce of the isotropic Universe via a relational time: We analyze the canonical quantum dynamics of the isotropic Universe in a
metric approach by adopting a self-interacting scalar field as relational time.
When the potential term is absent we are able to associate the the expanding
and collapsing dynamics of the Universe with the positive and negative
frequency modes that emerge in the Wheeler-DeWitt equation. On the other side,
when the potential term is present a non-zero transition amplitude from
positive to negative frequency states arises, as in the standard relativistic
scattering theory below the particle creation threshold. In particular, we are
able to compute the transition probability for an expanding Universe that
emerges from a collapsing regime both in the standard quantization procedure
and in the polymer formulation. The probability distribution results similar in
the two cases and its maximum takes place when the mean values of the momentum
essentially coincide in the in-going and out-going wave packets, as it would
take place in a semiclassical Big Bounce dynamics. | gr-qc |
Spinorial Wheeler-DeWitt wave functions inside black hole horizons: We revisit the solutions of the Wheeler-DeWitt (WDW) equation inside the
horizons of spherical black holes and planar topological black holes in
arbitrary dimensions. For these systems, the solutions of the equations are
found to have the same form. Therefore, Yeom's Annihilation-to-nothing
interpretation can be applied to each case. We have introduced the Dirac-type
WDW equations into quantum cosmology in a recent paper, so we also apply our
formulation to the quantum theory of the interior of the black hole in order to
obtain the solution of the spinorial wave function. The shape of the wave
packet of the spinorial WDW wave function indicates that the variation of
Yeom's interpretation holds in this scheme. | gr-qc |
Optical scalars in spherical spacetimes: Consider a spherically symmetric spacelike slice through a spherically
symmetric spacetime. One can derive a universal bound for the optical scalars
on any such slice. The only requirement is that the matter sources satisfy the
dominant energy condition and that the slice be asymptotically flat and regular
at the origin. This bound can be used to derive new conditions for the
formation of apparent horizons. The bounds hold even when the matter has a
distribution on a shell or blows up at the origin so as to give a conical
singularity. | gr-qc |
On multidimensional solutions in the Einstein-Gauss-Bonnet model with a
cosmological term: A D-dimensional gravitational model with Gauss-Bonnet and cosmological term
is considered. When ansatz with diagonal cosmological metrics is adopted, we
overview recent solutions for zero cosmological term and find new examples of
solutions for non-zero cosmological term and D = 8 with exponential dependence
of scale factors which describe an expansion of our 3-dimensional factor-space
and contraction of 4-dimensional internal space. | gr-qc |
Coincident Massless, Minimally Coupled Scalar Correlators on General
Cosmological Backgrounds: The coincidence limits of the massless, minimally coupled scalar propagator
and its first two derivatives have great relevance for the project of summing
up the leading logarithms induced by loops of inflationary gravitons. We use
dimensional regularization to derive good analytic approximations for the three
quantities on a general cosmological background geometry which underwent
inflation. | gr-qc |
Hot scalar radiation setting bounds on the curvature coupling parameter: This paper addresses the interplay between vacuum and thermal local averages
for massless scalar radiation near a plane wall of a large cavity where the
Dirichlet boundary condition is assumed to hold. The main result is that stable
thermodynamic equilibrium is possible only if the curvature coupling parameter
is restricted to a certain range. In more than three spacetime dimensions such
a range contains the conformal coupling, but it does not contain the minimal
coupling. Since this same range for possible values of the curvature coupling
parameter also applies to massive scalar radiation, it may be relevant in
settings where arbitrarily coupled scalar fields are present. | gr-qc |
Fingerprints of the cosmological constant: Folds in the profiles of the
axionic dark matter distribution in a dyon exterior: We consider the magnetic monopole in the axionic dark matter environment
(axionic dyon) in the framework of the Reissner - Nordstr\"om - de Sitter
model. Our aim is to study the distribution of the pseudoscalar (axion) and
electric fields near the so-called folds, which are characterized by the
profiles with the central minimum, the barrier on the left, and the maximum on
the right of this minimum. The electric field in the fold-like zones is shown
to change the sign twice, i.e., the electric structure of the near zone of the
axionic dyon contains the domain similar to a double electric layer. We have
shown that the described fold-like structures in the profile of the
gravitational potential, and in the profiles of the electric and axion fields
can exist, when the value of the dyon mass belongs to the interval enclosed
between two critical masses, which depend on the cosmological constant. | gr-qc |
Numerical relativity simulations of thick accretion disks around tilted
Kerr black holes: In this work we present 3D numerical relativity simulations of thick
accretion disks around tilted Kerr BH. We investigate the evolution of three
different initial disk models with a range of initial black hole spin
magnitudes and tilt angles. For all the disk-to-black hole mass ratios
considered (0.044-0.16) we observe significant black hole precession and
nutation during the evolution. This indicates that for such mass ratios,
neglecting the self-gravity of the disks by evolving them in a fixed background
black hole spacetime is not justified. We find that the two more massive models
are unstable against the Papaloizou-Pringle (PP) instability and that those
PP-unstable models remain unstable for all initial spins and tilt angles
considered, showing that the development of the instability is a very robust
feature of such PP-unstable disks. Our lightest model, which is the most
astrophysically favorable outcome of mergers of binary compact objects, is
stable. The tilt between the black hole spin and the disk is strongly modulated
during the growth of the PP instability, causing a partial global realignment
of black hole spin and disk angular momentum in the most massive model with
constant specific angular momentum l. For the model with non-constant l-profile
we observe a long-lived m=1 non-axisymmetric structure which shows strong
oscillations of the tilt angle in the inner regions of the disk. This effect
might be connected to the development of Kozai-Lidov oscillations. Our
simulations also confirm earlier findings that the development of the PP
instability causes the long-term emission of large amplitude gravitational
waves, predominantly for the l=m=2 multipole mode. The imprint of the BH
precession on the gravitational waves from tilted BH-torus systems remains an
interesting open issue that would require significantly longer simulations than
those presented in this work. | gr-qc |
Spinning super-massive objects in galactic nuclei up to $a_* > 1$: Nowadays we believe that a typical galaxy contains about $10^7$ stellar-mass
black holes and a single super-massive black hole at its center. According to
general relativity, these objects are characterized solely by their mass $M$
and by their spin parameter $a_*$. A fundamental limit for a black hole in
general relativity is the Kerr bound $|a_*| \le 1$, but the accretion process
can spin it up to $a_* \approx 0.998$. If a compact object is not a black hole,
the Kerr bound does not hold and in this letter I provide some evidences
suggesting that the accretion process could spin the body up to $a_* > 1$.
While this fact should be negligible for stellar-mass objects, some of the
super-massive objects at the center of galaxies may actually be super-spinning
bodies exceeding the Kerr bound. Such a possibility can be tested by
gravitational wave detectors like LISA or by sub-millimeter very long baseline
interferometry facilities. | gr-qc |
Impact of anti-symmetric contributions to signal multipoles in the
measurement of black-hole spins: Many current models for the gravitational-wave signal from precessing
black-hole binaries neglect an asymmetry in the $\pm m$ multipoles. The
asymmetry is weak, but is responsible for out-of-plane recoil, which for the
final black hole can be several thousand km/s. In this work we show that the
multipole asymmetry is also necessary to accurately measure the black-hole
spins. We consider synthetic signals calculated from the numerical relativity
surrogate model NRSur7dq4, which includes the multipole asymmetry, and measure
the signal parameters using two versions of the same model, one with and one
without the multipole asymmetry included. We find that in high
signal-to-noise-ratio observations where the spin magnitude and direction can
in principle be measured accurately, neglecting the multipole asymmetry can
result in biased measurements of these quantities. Measurements of the
black-hole masses and the standard aligned-spin combination $\chi_{\rm eff}$
are not in general strongly affected. As an illustration of the impact of the
multipole asymmetry on a real signal we consider the LVK observation
GW200129_065458, and find that the inclusion of the multipole asymmetry is
necessary to identify the binary as unequal-mass and a high in-plane spin in
the primary. | gr-qc |
Smarr formula for BTZ black holes in general three-dimensional gravity
models: Recent studies have presented the interpretation of thermodynamic enthalpy
for the mass of BTZ black holes and the corresponding Smarr formula. All these
are made in the background of three-dimensional (3D) general relativity. In
this paper, we extend such interpretation into general 3D gravity models. It is
found that the direct extension is unfeasible and some extra conditions are
required to preserve both the Smarr formula and the first law of black hole
thermodynamics. Thus, BTZ black hole thermodynamics enforces some constraints
for general 3D gravity models, and these constraints are consistent with all
previous discussions. | gr-qc |
Twisting Lightlike Solutions of the Kerr-Schild Class: Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and
the Kerr theorem we give a method to construct boosted Kerr geometries. In the
ultrarelativistic case this method yelds twisting solutions having, contrary to
the known pp-wave limiting solutions, a non-zero value of the total angular
momentum. The solutions show that twist plays a crucial role in removing
singularity and smoothing shock wave in the ultrarelativistic limit. Two
different physical situations are discussed. | gr-qc |
A stationary black hole must be axisymmetric in effective field theory: The black hole rigidity theorem asserts that a rotating stationary black hole
must be axisymmetric. This theorem holds for General Relativity with suitable
matter fields, in four or more dimensions. We show that the theorem can be
extended to any diffeomorphism invariant theory of vacuum gravity, assuming
that this is interpreted in the sense of effective field theory, with coupling
constants determined in terms of a ``UV scale'', and that the black hole
solution can locally be expanded as a power series in this scale. | gr-qc |
A Classical Sequential Growth Dynamics for Causal Sets: Starting from certain causality conditions and a discrete form of general
covariance, we derive a very general family of classically stochastic,
sequential growth dynamics for causal sets. The resulting theories provide a
relatively accessible ``half way house'' to full quantum gravity that possibly
contains the latter's classical limit (general relativity). Because they can be
expressed in terms of state models for an assembly of Ising spins living on the
relations of the causal set, these theories also illustrate how
non-gravitational matter can arise dynamically from the causal set without
having to be built in at the fundamental level. Additionally, our results bring
into focus some interpretive issues of importance for causal set dynamics, and
for quantum gravity more generally. | gr-qc |
Three problems of superfluid dark matter and their solution: In superfluid dark matter (SFDM), the phonon field plays a double role: It
carries the superfluid's energy density and it mediates the MOND-like phonon
force. We show that these two roles are in tension with each other on galactic
scales: A MOND-like phonon force is in tension with a superfluid in equilibrium
and with a significant superfluid energy density. To avoid these tensions, we
propose a model where the two roles are split between two different fields.
This also allows us to solve a stability problem in a more elegant way than
standard SFDM. We argue that the standard estimates for the size of a galaxy's
superfluid core need to be revisited. | gr-qc |
Non-relativistic limit of quantum field theory in inertial and
non-inertial frames and the Principle of Equivalence: We discuss the non-relativistic limit of quantum field theory in an inertial
frame, in the Rindler frame and in the presence of a weak gravitational field,
highlighting and clarifying several subtleties. We study the following topics:
(a) While the action for a relativistic free particle is invariant under the
Lorentz transformation, the corresponding action for a non-relativistic free
particle is not invariant under the Galilean transformation, but picks up extra
contributions at the end points. This leads to an extra phase in the
non-relativistic wave function under a Galilean transformation, which can be
related to the rest energy of the particle even in the non-relativistic limit.
(b) We show how the solution to the generally covariant Klein-Gordon equation
in a non-inertial frame, which has a time-dependent acceleration, reduces to
the quantum mechanical wave function in the presence of an appropriate
(time-dependent) gravitational field, in the non-relativistic limit. The extra
phase acquired by the non-relativistic wave function in an accelerated frame
actually arises from the gravitational time dilation and survives in the
non-relativistic limit. (c) We provide a detailed description of the
non-relativistic limit of the Feynman propagator in a weak gravitational field,
and discuss related issues. [Abridged Abstract] | gr-qc |
Thermodynamics of $f(R)$ Theories of Gravity: This paper starts from a toy model for inflation in a class of modified
theories of gravity in the metric formalism. Instead of the standard procedure
-- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from
a simple $\phi^2$ potential in the Einstein frame and investigate the
corresponding $f(R)$ in the former picture. The addition of an ad-hoc
Cosmological Constant in the Einstein frame leads to a Thermodynamical
interpretation of this physical system, which allows further insight on its
(meta)stability and evolution. | gr-qc |
Qualitative and Numerical Analysis of a Cosmological Model Based on an
Asymmetric Scalar Doublet with Minimal connections. IV. Numerical Modeling
and Types of Behavior of the Model: On the basis of a qualitative and numerical analysis of a cosmological model
based on an asymmetric scalar doublet of nonlinear, minimally interacting
scalar fields -- one classical and one phantom, peculiarities of the behavior
of the model near zero energy hypersurfaces have been revealed. Numerical
models have been constructed, in which the dynamical system has limit cycles on
the zero-energy hypersurfaces. Three types of behavior of the cosmological
model have been distinguished, configured by the fundamental constants of the
scalar fields and the initial conditions. It is shown that over a wide sector
of values of the fundamental constants and initial conditions, the cosmological
models have a tendency to adhere to the zero-energy hypersurfaces corresponding
to 4-dimensional Euclidean space. | gr-qc |
GUP-corrected $Λ$CDM cosmology: In this study, we investigate the effect of the generalized uncertainty
principle on the $\Lambda$CDM cosmological model. Using quantum corrected Unruh
effect and Verlinde's entropic gravity idea, we find Planck-scale corrected
Friedmann equations with a cosmological constant. These results modify the
$\Lambda$CDM cosmology. | gr-qc |
Echoes of Compact Objects in Scalar-Tensor Theories of Gravity: Scalar-tensor theory predicts solutions to the gravitational field equations
which describe compact objects in the presence of a non-minimally coupled
scalar field to the Einstein tensor. These objects are black holes with scalar
hair and wormholes supporting scalar phantom matter. The evolution of test
fields in fixed asymptotically-flat backgrounds of exotic compact objects leads
to the formation of echoes in the ringdown signal, which designate the
existence of trapping regions close to the event horizon. Here, we consider
minimally-coupled test scalar fields propagating on compact object solutions of
the Horndeski action, which possess an effective cosmological constant, leading
to anti-de Sitter asymptotics, and show that echoes can form in the ringdown
waveform due to the entrapment of test fields between the photon sphere and the
effective asymptotic boundary. Although the presence of an event horizon leads
to the usual echoes with decaying amplitude, signifying modal stability of the
scalarized black hole considered, we find that test scalar fields propagating
on a scalarized wormhole solution give rise to echoes of constant and equal
amplitude to that of the initial ringdown, indicating the existence of normal
modes. Finally, we find that, near extremality, the test field exhibits a
concatenation of echoes; the primary ones are associated with the trapping
region between the photon sphere and the effective anti-de Sitter boundary
while the secondary ones are linked to the existence of a potential well at the
throat of the wormhole. | gr-qc |
The Superradiant Instability in AdS: We consider the intermediate and end state behavior of the superradiantly
perturbed Kerr black hole. Superradiant scattering in an asymptotically flat
background is considered first. The case of a Kerr black hole in an Anti
de-Sitter background is then discussed. Specifically we review what is known
about the superradiant instability arising in AdS and its possible end state
behavior. | gr-qc |
Quantum black hole without singularity: We discuss the quantization of a spherical dust shell in a rigorous manner.
Classically, the shell can collapse to form a black hole with a singularity. In
the quantum theory, we construct a well-defined self-adjoint extension for the
Hamilton operator. As a result, the evolution is unitary and the singularity is
avoided. If we represent the shell initially by a narrow wave packet, it will
first contract until it reaches the region where classically a black hole would
form, but then re-expands to infinity. In a way, the state can be interpreted
as a superposition of a black hole with a white hole. | gr-qc |
Binary Inspirals in Nordström's Second Theory: We investigate Nordstr\"om's second theory of gravitation, with a focus on
utilizing it as a testbed for developing techniques in numerical relativity.
Numerical simulations of inspiraling compact star binaries are performed for
this theory, and compared to the predictions of semi-analytic calculations
(which are similar to Peters and Mathews' results for GR). The simulations are
based on a co-rotating spherical coordinate system, where both finite
difference and pseudo-spectral methods are used. We also adopt the "Hydro
without Hydro" approximation, and the Weak Radiation Reaction approximation
when the orbital motion is quasi-circular. We evolve a binary with
quasi-circular initial data for hundreds of orbits and find that the resulting
inspiral closely matches the 1/4 power law profile given by the semi-analytical
calculations. We additionally find that an eccentric binary circularizes and
precesses at the expected rates. The methods investigated thus provide a
promising line of attack for the numerical modeling of long binary inspirals in
general relativity. | gr-qc |
Constraining spacetime torsion with the Moon and Mercury: We report a search for new gravitational physics phenomena based on
Einstein-Cartan theory of General Relativity including spacetime torsion.
Starting from the parametrized torsion framework of Mao, Tegmark, Guth and
Cabi, we analyze the motion of test bodies in the presence of torsion, and in
particular we compute the corrections to the perihelion advance and to the
orbital geodetic precession of a satellite. We describe the torsion field by
means of three parameters, and we make use of the autoparallel trajectories,
which in general may differ from geodesics when torsion is present. We derive
the equations of motion of a test body in a spherically symmetric field, and
the equations of motion of a satellite in the gravitational field of the Sun
and the Earth. We calculate the secular variations of the longitudes of the
node and of the pericenter of the satellite. The computed secular variations
show how the corrections to the perihelion advance and to the orbital de Sitter
effect depend on the torsion parameters. All computations are performed under
the assumptions of weak field and slow motion. To test our predictions, we use
the measurements of the Moon geodetic precession from lunar laser ranging data,
and the measurements of Mercury's perihelion advance from planetary radar
ranging data. These measurements are then used to constrain suitable linear
combinations of the torsion parameters. | gr-qc |
Chaos and Universality in the Dynamics of Inflationary Cosmologies: We describe a new statistical pattern in the chaotic dynamics of closed
inflationary cosmologies, associated with the partition of the Hamiltonian
rotational motion energy and hyperbolic motion energy pieces, in a linear
neighborhood of the saddle-center present in the phase space of the models. The
hyperbolic energy of orbits visiting a neighborhood of the saddle-center has a
random distribution with respect to the ensemble of initial conditions, but the
associated histograms define a statistical distribution law of the form $p(x) =
C x^{-\gamma}$, for almost the whole range of hyperbolic energies considered.
We present numerical evidence that $\gamma$ determines the dimension of the
fractal basin boundaries in the ensemble of initial conditions. This
distribution is universal in the sense that it does not depend on the
parameters of the models and is scale invariant. We discuss possible physical
consequences of this universality for the physics of inflation.tribution law of
the form $p(x) = C x^{-\gamma}$, for almost the whole range of hyperbolic
energies considered. We present numerical evidence that $\gamma$ determines the
dimension of the fractal basin boundaries in the ensemble of initial
conditions. This distribution is universal in the sense that it does not depend
on the parameters of the models and is scale invariant. We discuss possible
physical consequences of this universality for the physics of inflation. | gr-qc |
Production and decay of evolving horizons: We consider a simple physical model for an evolving horizon that is strongly
interacting with its environment, exchanging arbitrarily large quantities of
matter with its environment in the form of both infalling material and outgoing
Hawking radiation. We permit fluxes of both lightlike and timelike particles to
cross the horizon, and ask how the horizon grows and shrinks in response to
such flows. We place a premium on providing a clear and straightforward
exposition with simple formulae.
To be able to handle such a highly dynamical situation in a simple manner we
make one significant physical restriction, that of spherical symmetry, and two
technical mathematical restrictions: (1) We choose to slice the spacetime in
such a way that the space-time foliations (and hence the horizons) are always
spherically symmetric. (2) Furthermore we adopt Painleve-Gullstrand coordinates
(which are well suited to the problem because they are nonsingular at the
horizon) in order to simplify the relevant calculations.
We find particularly simple forms for surface gravity, and for the first and
second law of black hole thermodynamics, in this general evolving horizon
situation. Furthermore we relate our results to Hawking's apparent horizon,
Ashtekar et al's isolated and dynamical horizons, and Hayward's trapping
horizons. The evolving black hole model discussed here will be of interest,
both from an astrophysical viewpoint in terms of discussing growing black
holes, and from a purely theoretical viewpoint in discussing black hole
evaporation via Hawking radiation. | gr-qc |
Possible test of local Lorentz invariance from $τ$ decays: We analyze the possibility of testing local Lorentz invariance from the
observation of tau decays. Future prospects of probing distances below the
electroweak characteristic scale are discussed. | gr-qc |
Polymer Parametrised Field Theory: Free scalar field theory on 2 dimensional flat spacetime, cast in
diffeomorphism invariant guise by treating the inertial coordinates of the
spacetime as dynamical variables, is quantized using LQG type `polymer'
representations for the matter field and the inertial variables. The quantum
constraints are solved via group averaging techniques and, analogous to the
case of spatial geometry in LQG, the smooth (flat) spacetime geometry is
replaced by a discrete quantum structure. An overcomplete set of Dirac
observables, consisting of (a) (exponentials of) the standard free scalar field
creation- annihilation modes and (b) canonical transformations corresponding to
conformal isometries, are represented as operators on the physical Hilbert
space. None of these constructions suffer from any of the `triangulation'
dependent choices which arise in treatments of LQG. In contrast to the standard
Fock quantization, the non- Fock nature of the representation ensures that the
algebra of conformal isometries as well as that of spacetime diffeomorphisms
are represented in an anomaly free manner. Semiclassical states can be analysed
at the gauge invariant level. It is shown that `physical weaves' necessarily
underly such states and that such states display semiclassicality with respect
to, at most, a countable subset of the (uncountably large) set of observables
of type (a). The model thus offers a fertile testing ground for proposed
definitions of quantum dynamics as well as semiclassical states in LQG. | gr-qc |
Observational constraints on tachyonic chameleon dark energy model: It has been recently shown that tachyonic chameleon model of dark energy in
which tachyon scalar field non-minimally coupled to the matter admits stable
scaling attractor solution that could give rise to the late-time accelerated
expansion of the universe and hence alleviate the coincidence problem. In the
present work, we use data from Type Ia supernova (SN Ia) and Baryon Acoustic
Oscillations to place constraints on the model parameters. In our analysis we
consider in general exponential and non-exponential forms for the non-minimal
coupling function and tachyonic potential and show that the scenario is
compatible with observations. | gr-qc |
Comments on "Solar System constraints to general f(R) gravity": We comment on, and complete, the analysis of the weak field limit of metric
f(R) gravity in T. Chiba, T.L. Smith, and A.L. Erickcek, Phys. Rev. D 75,
124014 (2007). | gr-qc |
Static Black Holes of Metric-Affine Gravity in the Presence of Matter: We investigate spherically symmetric and static gravitational fields
representing black hole configurations in the framework of metric-affine gauge
theories of gravity (MAG) in the presence of different matter fields. It is
shown that in the triplet ansatz sector of MAG, black hole configurations in
the presence of non-Abelian matter fields allow the existence of black hole
hair. We analyze several cases of matter fields characterized by the presence
of hair and for all of them we show the validity of the no short hair
conjecture. | gr-qc |
Slowly decaying ringdown of a rapidly spinning black hole II: Inferring
the masses and spins of supermassive black holes with LISA: Electromagnetic observations reveal that almost all galaxies have
supermassive black holes (SMBHs) at their centers, but their properties,
especially their spins, are not fully understood. Some of the authors have
recently shown [Oshita and Tsuna (2023)] that rapid spins of $>0.9$, inferred
for masses around $10^7\ M_\odot$ from observations of local SMBHs and
cosmological simulations, source {\it long-lived} ringdowns that enhance the
precision of black hole spectroscopy to test gravity in the near-extreme Kerr
spacetime. In this work, we estimate the statistical errors in the SMBH
mass-spin inference in anticipation of the LISA's detection of extreme
mass-ratio mergers. We show that for rapidly spinning SMBHs, more precise mass
and spin measurements are expected due to the excitations of higher angular
modes. For a near-extremal SMBH of mass $10^7M_\odot$ merging with a smaller BH
with mass ratio $10^{-3}$ at a luminosity distance of $\lesssim
10\:\mathrm{Gpc}$ (redshift $z \lesssim 1.37$), the measurement errors in the
mass and spin of the SMBH would be $\sim 1\:\mathrm{\%}$ and $\sim
10^{-1}\:\mathrm{\%}$ respectively. | gr-qc |
Restoration of four-dimensional diffeomorphism covariance in canonical
general relativity: An intrinsic Hamilton-Jacobi approach: Classical background independence is reflected in Lagrangian general
relativity through covariance under the full diffeomorphism group. We show how
this independence can be maintained in a Hamilton-Jacobi approach that does not
accord special privilege to any geometric structure. Intrinsic spacetime
curvature based coordinates grant equal status to all geometric backgrounds.
They play an essential role as a starting point for inequivalent semi-classical
quantizations. The scheme calls into question Wheeler's geometrodynamical
approach and the associated Wheeler-DeWitt equation in which three-metrics are
featured geometrical objects. The formalism deals with variables that are
manifestly invariant under the full diffeomorphism group. Yet, perhaps
paradoxically, the liberty in selecting intrinsic coordinates is precisely as
broad as is the original diffeomorphism freedom. We show how various ideas from
the past five decades concerning the true degrees of freedom of general
relativity can be interpreted in light of this new constrained Hamiltonian
description. In particular, we show how the Kucha\v{r} multi-fingered time
approach can be understood as a means of introducing full four-dimensional
diffeomorphism invariants. Every choice of new phase space variables yields new
Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic
Schr\"odinger equations. We show how to implement this freedom by canonical
transformation of the intrinsic Hamiltonian. We also reinterpret and rectify
significant work by B. Dittrich on the construction of `Dirac observables'. | gr-qc |
Analysis of the Yukawa gravitational potential in $f(R)$ gravity II:
relativistic periastron advance: Alternative theories of gravity may serve to overcame several shortcomings of
the standard cosmological model but, in their weak field limit, General
Relativity must be recovered so as to match the tight constraints at the Solar
System scale. Therefore, testing such alternative models at scales of stellar
systems could give a unique opportunity to confirm or rule them out. One of the
most straightforward modifications is represented by analytical $f(R)$-gravity
models that introduce a Yukawa-like modification to the Newtonian potential
thus modifying the dynamics of particles. Using the geodesics equations, we
have illustrated the amplitude of these modifications. First, we have
integrated numerically the equations of motion showing the orbital precession
of a particle around a massive object. Second, we have computed an analytic
expression for the periastron advance of systems having their semi-major axis
much shorter than the Yukawa-scale length. Finally, we have extended our
results to the case of a binary system composed of two massive objects. Our
analysis provides a powerful tool to obtain constraints on the underlying
theory of gravity using current and forthcoming datasets. | gr-qc |
Numerical Analysis of the Wave Function of the Multidimensional Universe: In the framework of the Hartle-Hawking no-boundary proposal, we investigate
quantum creation of the multidimensional universe with the cosmological
constant $\Lambda$ but without matter fields. In this paper we solved the
Wheeler-de Witt equation numerically. We find that the universe in which both
of the spaces expand exponentially is the most probable in this model. | gr-qc |
A formalism for magnon gravitational wave detectors: In order to detect high frequency gravitational waves, we need a new
detection method. In this paper, we develop a formalism for a gravitational
wave detector using magnons in a cavity. Using Fermi normal coordinates and
taking the non-relativistic limit, we obtain a Hamiltonian for magnons in
gravitational wave backgrounds. Given the Hamiltonian, we show how to use the
magnons for detecting high frequency gravitational waves. Furthermore, as a
demonstration of the magnon gravitational wave detector, we give upper limits
on GHz gravitational waves by utilizing known results of magnon experiments for
an axion dark matter search. | gr-qc |
Covariant Vortex In Superconducting-Superfluid-Normal Fluid Mixtures
with Stiff Equation of State: The integrals of motion for a cylindrically symmetric stationary vortex are
obtained in a covariant description of a mixture of interacting
superconductors, superfluids and normal fluids. The relevant integrated
stress-energy coefficients for the vortex with respect to a vortex-free
reference state are calculated in the approximation of a ``stiff'', i.e. least
compressible, relativistic equation of state for the fluid mixture. As an
illustration of the foregoing general results, we discuss their application to
some of the well known examples of ``real'' superfluid and superconducting
systems that are contained as special cases. These include Landau's two-fluid
model, uncharged binary superfluid mixtures, rotating conventional
superconductors and the superfluid neutron-proton-electron plasma in the outer
core of neutron stars. | gr-qc |
Generalized (2+1) dimensional black hole by Noether symmetry: We use the Noether symmetry approach to find $f(R)$ theory of $(2+1)$
dimensional gravity and $(2+1)$ dimensional black hole solution consistent with
this $f(R)$ gravity and the associated symmetry. We obtain $f({R})=D_1
R({n}/{n+1})({R}/{K})^{1/n}+D_2 R+D_3$, where the constant term $D_3$ plays no
dynamical role. Then, we find general spherically symmetric solution for this
$f(R)$ gravity which is potentially capable of being as a black hole. Moreover,
in the special case $D_1=0, D_2={1}$, namely $f(R)=R+D_3$, we obtain a
generalized BTZ black hole which, other than common conserved charges $m$ and
$J$, contains a new conserved charge Q. It is shown that this conserved charge
corresponds to the freedom in the choice of the constant term $D_3$ and
represents symmetry of the action under the transformation $R \rightarrow
R'=R+D_3$ along the killing vector $\partial_{R}$. The ordinary BTZ black hole
is obtained as the special case where $D_3$ is {\it fixed} to be proportional
to the infinitesimal cosmological constant and consequently the symmetry is
broken via Q=0. We study the thermodynamics of the generalized BTZ black hole
and show that its entropy can be described by the Cardy-Verlinde formula. | gr-qc |
TiO2 doping effect on reflective coating mechanical loss for
gravitational wave detection at low temperature: We measured the mechanical loss of a dielectric multilayer reflective coating
(ion-beam-sputtered SiO2 and Ta2O5) with and without TiO2 on sapphire disks
between 6 and 77 K. The measured loss angle exhibited a temperature dependence,
and the local maximum was found at approximately 20 K. This maximum was
7.0*10^(-4) (with TiO2) and 7.7*10^(-4) (without TiO2), although the previous
measurement for the coating on sapphire disks showed almost no temperature
dependence (Phys. Rev. D 74 022002 (2006)). We evaluated the coating thermal
noise in KAGRA and discussed future investigation strategies. | gr-qc |
Tilt-to-length coupling in LISA Pathfinder: analytical modelling: Tilt-to-length coupling was the limiting noise source in LISA Pathfinder
between 20 and 200 mHz before subtraction in post-processing. To prevent the
adding of sensing noise to the data by the subtraction process, the success of
this strategy depended on a previous direct noise reduction by test mass
alignment. The exact dependency of the level of tilt-to-length coupling on the
set-points of LISA Pathfinder's test masses was not understood until the end of
the mission. Here, we present, for the first time, an analytical tilt-to-length
coupling model that describes the coupling noise changes due to the
realignments. We report on the different mechanisms, namely the lever arm and
piston effect as well as the coupling due to transmissive components, and how
they contribute to the full coupling. Further, we show that a pure geometric
model would not have been sufficient to describe the coupling in LISA
Pathfinder. Therefore, we model also the non-geometric tilt-to-length noise
contributions. For the resulting coupling coefficients of the full model, we
compute the expected error bars based on the known individual error sources.
Also, we validated the analytical model against numerical simulations. A
detailed study and thorough understanding of this noise are the basis for a
successful analysis of the LISA Pathfinder data with respect to tilt-to-length
coupling. | gr-qc |
Einstein-Schrodinger theory using Newman-Penrose tetrad formalism: The Einstein-Schrodinger theory is modified to include a large cosmological
constant caused by zero-point fluctuations. This ``extrinsic'' cosmological
constant which multiplies the symmetric metric is assumed to be nearly
cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the
nonsymmetric fundamental tensor, such that the total cosmological constant is
consistent with measurement. This modified Einstein-Schrodinger theory is
expressed in Newman-Penrose form, and tetrad methods are used to confirm that
it closely approximates ordinary general relativity and electromagnetism. A
solution for the connections in terms of the fundamental tensor is derived in
the tetrad frame. The tetrad form of an exact electric monopole solution is
shown to approximate the Reissner-Nordstrom solution and to be of Petrov
type-D. | gr-qc |
Overview of the BlockNormal Event Trigger Generator: In the search for unmodeled gravitational wave bursts, there are a variety of
methods that have been proposed to generate candidate events from time series
data. Block Normal is a method of identifying candidate events by searching for
places in the data stream where the characteristic statistics of the data
change. These change-points divide the data into blocks in which the
characteristics of the block are stationary. Blocks in which these
characteristics are inconsistent with the long term characteristic statistics
are marked as Event-Triggers which can then be investigated by a more
computationally demanding multi-detector analysis. | gr-qc |
Analyzing black-hole ringdowns: A perturbed black hole rings down by emitting gravitational waves in tones
with specific frequencies and durations. Such tones encode prized information
about the geometry of the source spacetime and the fundamental nature of
gravity, making the measurement of black hole ringdowns a key goal of
gravitational wave astronomy. However, this task is plagued by technical
challenges that invalidate the naive application of standard data analysis
methods and complicate sensitivity projections. In this paper, we provide a
comprehensive account of the formalism required to properly carry out ringdown
analyses, examining in detail the foundations of recent observational results,
and providing a framework for future measurements. We build on those insights
to clarify the concepts of ringdown detectability and resolvability -- touching
on the drawbacks of both Bayes factors and naive Fisher matrix approaches --
and find that overly pessimistic heuristics have led previous works to
underestimate the role of ringdown overtones for black hole spectroscopy. We
put our framework to work on the analysis of a variety of simulated signals in
colored noise, including analytic injections and a numerical relativity
simulation consistent with GW150914. We demonstrate that we can use tones of
the quadrupolar angular harmonic to test the no-hair theorem at current
sensitivity, with precision comparable to published constraints from real data.
Finally, we assess the role of modeling systematics, and project measurements
for future, louder signals. We release ringdown, a Python library for analyzing
black hole ringdowns using the the methods discussed in this paper, under a
permissive open-source license at https://github.com/maxisi/ringdown | gr-qc |
On Fast Travel through spherically symmetric spacetimes: In a static spacetime, the Killing time can be used to measure the time
required for signals or objects to propagate between two of its orbits. By
further restricting to spherically symmetric cases, one obtains a natural
association between these orbits and timelike lines in Minkowski space. We
prove a simple theorem to the effect that in any spacetime satisfying the weak
energy condition the above signaling time is, in this sense, no faster than
that for a corresponding signal in Minkowski space. The theorem uses a
ormalization of Killing time appropriate to an observer at infinity. We then
begin an investigation of certain related but more local questions by studying
particular families of spacetimes in detail. Here we are also interested in
restrictions imposed by the dominant energy condition. Our examples suggest
that signaling in spacetimes satisfying this stronger energy condition may be
significantly slower than the fastest spacetimes satisfying only the weak
energy condition. | gr-qc |
Characterization of the gravitational wave spectrum from sound waves
within the sound shell model: We compute the gravitational wave (GW) spectrum sourced by sound waves
produced during a first-order phase transition in the radiation-dominated
epoch. The correlator of the velocity field is evaluated in accordance with the
sound shell model. In our derivation we include the effects of the expansion of
the Universe, which are relevant in particular for sourcing processes whose
time duration is comparable with the Hubble time. Our results show a causal
growth at small frequencies, $\Omega_{\rm GW} \sim k^3$, possibly followed by a
linear regime $\Omega_{\rm GW} \sim k$ at intermediate $k$, depending on the
phase transition parameters. Around the peak, we find a steep growth that
approaches the $k^9$ scaling found within the sound shell model. The resulting
bump around the peak of the GW spectrum may represent a distinctive feature of
GWs produced from acoustic motion. Nothing similar has been observed for
vortical (magneto)hydrodynamic turbulence. Nevertheless, we find that the $k^9$
scaling is less extended than expected in the literature, and it does not
necessarily appear. The dependence on the duration of the source, $\delta
\tau_{\rm fin}$, is quadratic at small frequencies $k$, and proportional to
$\ln^2 (1 + \delta \tau_{\rm fin} H_*)$ for an expanding Universe. At
frequencies around the peak, the growth is suppressed by a factor $\Upsilon = 1
- 1/(1 + \delta \tau_{\rm fin} {H}_*)$ that becomes linear when the GW source
is short. We discuss in which cases the dependence on the source duration is
linear or quadratic for stationary processes. This affects the amplitude of the
GW spectrum, both in the causality tail and at the peak, showing that the
assumption of stationarity is a very relevant one, as far as the GW spectral
shape is concerned. Finally, we present a general semi-analytical template of
the resulting GW spectrum, as a function of the parameters of the phase
transition. | gr-qc |
Non-commutative and commutative vacua effects in a scalar torsion
scenario: In this work, the effects of non-commutative and commutative vacua on the
phase space generated by a scalar field in a scalar torsion scenario are
investigated. For both classical and quantum regimes, the commutative and
non-commutative cases are compared. To take account the effects of
non-commutativity, two well known non-commutative parameters, $\theta$ and
$\beta,$ are introduced. It should be emphasized, the effects of $\beta$ which
is related to momentum sector has more key role in comparison to $\theta$ which
is related to space sector. Also the different boundary conditions and
mathematical interpretations of non-commutativity are explored. | gr-qc |
Asymptotic behavior of a matter filled universe with exotic topology: The ADM formalism together with a constant mean curvature (CMC) temporal
gauge is used to derive the monotonic decay of a weak Lyapunov function of the
Einstein dynamical equations in an expanding universe with a positive
cosmological constant and matter sources satisfying suitable energy conditions.
While such a Lyapunov function does not, in general, represent a true
Hamiltonian of the matter-coupled gravity dynamics (unlike in the vacuum case
when it does), it can nevertheless be used to study the asymptotic behavior of
the spacetimes. The Lyapunov function attains its infimum only in the limit
that the matter sources be `turned off` or, at least, become asymptotically
negligible provided that the universe model does not re-collapse and form
singularities. Later we specialize our result to the case of a perfect fluid
which satisfies the desired energy conditions. However, even in this special
case, we show using Shutz's velocity potential formalism cast into Hamiltonian
form that unlike the vacuum spacetimes (with or without a positive cosmological
constant), construction of a true Hamiltonian for the dynamics in constant mean
curvature temporal gauge is difficult and therefore the Lyapunov function does
not have a straightforward physical interpretation. Nevertheless, we show, for
the fluid with equation of state $P=(\gamma-1)\rho$ ($1\leq\gamma\leq2$), that
the general results obtained hold true and the infimum of the weak Lyapunov
function can be related to the Sigma constant, a topological invariant of the
manifold. Utilizing these results, some general conclusions are drawn regarding
the asymptotic state of the universe and the dynamical control of the allowed
spatial topologies in the cosmological models. | gr-qc |
Gravitational Collapse of Anisotropic Compact Stars in Modified $ f(R) $
Gravity: The physically realistic model of compact stars undergoing gravitational
collapse in $ f(R) $ gravity has been developed. We consider a more general
model $ R + f(R) = R + k R^m $ and describe the interior space-time of
gravitationally collapsing stars with separable-form of metric admitting
homothetic killing vector. We then investigate the junction conditions to match
the interior space-time with exterior space-time. Considering all junction
conditions, we find analytical solutions describing interior space-time metric,
energy density, pressures, and heat flux density of the compact stars
undergoing gravitational collapse. We impose the energy conditions to the model
for describing the realistic collapse of physically possible matter
distribution for particular models of $GR$, $ R+k R^2 $ and $ R+k R^4 $
gravity. The comprehensive graphical analysis of all energy conditions show
that the model is physically acceptable and realistic. We additionally
investigate the physical properties of collapsing stars which are useful to
decipher the inherent nature of such gravitationally collapsing stars. | gr-qc |
Exact Cosmological Models with the Yang - Mills Fields on Lyra Manifold: The present study deals with the Friedmann-Robertson-Walker cosmological
models of the Yang-Mills (YM) fields in Lyra geometry. The energy-momentum
tensor of the YM fields for our models is obtained with the help of exact
solution for the corresponding YM equations subject to their minimal coupling
to gravity. Two specific exact solutions of the model are obtained regarding
the effective equation of state and the exponential law of expansion. Some
physical and geometrical behavior of the model are also discussed. | gr-qc |
On the Properties of Exact Solutions Endowed with Negative Mass: It is shown that various pathological properties of spacetimes can be
explained by the presence of negative mass, including the cases when the total
mass of the solution is a positive quantity. As an illustration, we consider
several well-known stationary axisymmetric vacuum and electrovac solutions of
the Einstein-Maxwell equations. Our investigation naturally leads to a critique
of the known maximal extensions of the Kerr and Kerr-Newman spacetimes which
turn out to be neither analytic nor physically meaningful. | gr-qc |
Background Independent Quantum Gravity: A Status Report: The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it. | gr-qc |
Exact solutions for compact stars with CFL quark matter: The search for the true ground state of the dense matter remains open since
Bodmer, Terazawa and other raised the possibility of stable quarks, boosted by
Witten's $strange$ $matter$ hypothesis in 1984. Within this proposal, the
strange matter is assumed to be composed of $strange$ quarks in addition to the
usual $up$s and $down$s, having an energy per baryon lower than the strangeless
counterpart, and even lower than that of nuclear matter. In this sense, neutron
stars should actually be strange stars. Later work showed that a paired,
symmetric in flavor, color-flavor locked (CFL) state would be preferred to the
one without any pairing for a wide range of the parameters (gap $\Delta$,
strange quark mass $m_s$, and bag constant B). We use an approximate, yet very
accurate, CFL equation of state (EoS) that generalizes the MIT bag model to
obtain two families of exact solutions for the static Einstein field equations
constructing families anisotropic compact relativistic objects. In this
fashion, we provide exact useful solutions directly connected with
microphysics. | gr-qc |
The quantum theory of scalar fields on the de Sitter expanding universe: New quantum modes of the free scalar field are derived in a special
time-evolution picture that may be introduced in moving charts of de Sitter
backgrounds. The wave functions of these new modes are solutions of the
Klein-Gordon equation and energy eigenfunctions, defining the energy basis.
This completes the scalar quantum mechanics where the momentum basis is
well-known from long time. In this enlarged framework the quantization of the
scalar field can be done in canonical way obtaining the principal conserved
one-particle operators and the Green functions. | gr-qc |
The Effacing Principle in the Post-Newtonian Celestial Mechanics: First post-Newtonian (PN) approximation of the scalar-tensor theory of
gravity is used to discuss the effacing principle in N-body system, that is
dependence of equations of motion of spherically-symmetric bodies comprising
the system on their internal structure. We demonstrate that the effacing
principle is violated by terms which are proportional to the second order
rotational moment of inertia of each body coupled with \beta-1, where \beta is
the measure of non-linearity of gravitational field. In case of general
relativity, where \beta=1, the effacing principle is violated by terms being
proportional to the rotational moment of inertia of the forth order. For
systems made of neutron stars (NS) and/or black holes (BH) these terms
contribute to the orbital equations of motion at the level of the third and
fifth PN approximation respectively. | gr-qc |
Dynamical system analysis for DBI dark energy interacting with dark
matter: A dynamical system analysis related to Dirac Born Infeld (DBI) cosmological
model has been investigated in this present work. For spatially flat FRW space
time, the Einstein field equation for DBI scenario has been used to study the
dynamics of DBI dark energy interacting with dark matter. The DBI dark energy
model is considered as a scalar field with a nonstandard kinetic energy term.
An interaction between the DBI dark energy and dark matter is considered
through a phenomenological interaction between DBI scalar field and the dark
matter fluid. The field equations are reduced to an autonomous dynamical system
by a suitable redefinition of the basic variables. The potential of the DBI
scalar field is assumed to be exponential. Finally, critical points are
determined, their nature have been analyzed and corresponding cosmological
scenario has been discussed. | gr-qc |
Towards resolution of anisotropic cosmological singularity in infinite
derivative gravity: In this paper, we will show that the equations of motion of the quadratic in
curvature, ghost free, infinite derivative theory of gravity will not permit an
anisotropic collapse of a homogeneous Universe for a Kasner-type vacuum
solution. | gr-qc |
Lower bound on the mass of a black hole: We consider gravity coupled to a massive field whose Compton's wavelength is
far larger than the Planck's length. In the low energy effective action for
gravity, thus, it is the perturbation in the Compton's wavelength that breaks
first as the sub-sub-leading quantum perturbation grows stronger. When this
break occurs, we can not trust the perturbative information about the form of
the low energy effective action. We translate this break into the lowest limit
on the mass of a classical black hole. In D=4, using the electron's mass, this
requires the black hole to be heavier than 10^{14} kg. | gr-qc |
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