448 research outputs found
Remarks on effective action and entanglement entropy of Maxwell field in generic gauge
We analyze the dependence of the effective action and the entanglement
entropy in the Maxwell theory on the gauge fixing parameter in
dimensions. For a generic value of the corresponding vector operator is
nonminimal. The operator can be diagonalized in terms of the transverse and
longitudinal modes. Using this factorization we obtain an expression for the
heat kernel coefficients of the nonminimal operator in terms of the
coefficients of two minimal Beltrami-Laplace operators acting on 0- and
1-forms. This expression agrees with an earlier result by Gilkey et al. Working
in a regularization scheme with the dimensionful UV regulators we introduce
three different regulators: for transverse, longitudinal and ghost modes,
respectively. We then show that the effective action and the entanglement
entropy do not depend on the gauge fixing parameter provided the certain
(-dependent) relations are imposed on the regulators. Comparing the
entanglement entropy with the black hole entropy expressed in terms of the
induced Newton's constant we conclude that their difference, the so-called
Kabat's contact term, does not depend on the gauge fixing parameter . We
consider this as an indication of gauge invariance of the contact term.Comment: 15 pages; v2: typos in eqs. (31), (32), (34), (36) corrected;
discussion in section 6 expande
Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
Euclidean gravity method has been successful in computing logarithmic
corrections to extremal black hole entropy in terms of low energy data, and
gives results in perfect agreement with the microscopic results in string
theory. Motivated by this success we apply Euclidean gravity to compute
logarithmic corrections to the entropy of various non-extremal black holes in
different dimensions, taking special care of integration over the zero modes
and keeping track of the ensemble in which the computation is done. These
results provide strong constraint on any ultraviolet completion of the theory
if the latter is able to give an independent computation of the entropy of
non-extremal black holes from microscopic description. For Schwarzschild black
holes in four space-time dimensions the macroscopic result seems to disagree
with the existing result in loop quantum gravity.Comment: LaTeX, 40 pages; corrected small typos and added reference
Gravitational Chern-Simons Lagrangians and black hole entropy
We analyze the problem of defining the black hole entropy when Chern-Simons
terms are present in the action. Extending previous works, we define a general
procedure, valid in any odd dimensions both for purely gravitational CS terms
and for mixed gauge-gravitational ones. The final formula is very similar to
Wald's original formula valid for covariant actions, with a significant
modification. Notwithstanding an apparent violation of covariance we argue that
the entropy formula is indeed covariant.Comment: 39 page
Logarithmic correction to BH entropy as Noether charge
We consider the role of the type-A trace anomaly in static black hole
solutions to semiclassical Einstein equation in four dimensions. Via Wald's
Noether charge formalism, we compute the contribution to the entropy coming
from the anomaly induced effective action and unveil a logarithmic correction
to the Bekenstein-Hawking area law.
The corrected entropy is given by a seemingly universal formula involving the
coefficient of the type-A trace anomaly, the Euler characteristic of the
horizon and the value at the horizon of the solution to the uniformization
problem for Q-curvature. Two instances are examined in detail: Schwarzschild
and a four-dimensional massless topological black hole. We also find agreement
with the logarithmic correction due to one-loop contribution of conformal
fields in the Schwarzschild background.Comment: 14 pages, JHEP styl
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
This article is meant as a summary and introduction to the ideas of effective
field theory as applied to gravitational systems.
Contents:
1. Introduction
2. Effective Field Theories
3. Low-Energy Quantum Gravity
4. Explicit Quantum Calculations
5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living
Reviews of Relativit
Entanglement Entropy for Singular Surfaces
We study entanglement entropy for regions with a singular boundary in higher
dimensions using the AdS/CFT correspondence and find that various singularities
make new universal contributions. When the boundary CFT has an even spacetime
dimension, we find that the entanglement entropy of a conical surface contains
a term quadratic in the logarithm of the UV cut-off. In four dimensions, the
coefficient of this contribution is proportional to the central charge 'c'. A
conical singularity in an odd number of spacetime dimensions contributes a term
proportional to the logarithm of the UV cut-off. We also study the entanglement
entropy for various boundary surfaces with extended singularities. In these
cases, similar universal terms may appear depending on the dimension and
curvature of the singular locus.Comment: 66 pages,4 figures. Some typos are removed and a reference is adde
Warped black holes in 3D general massive gravity
We study regular spacelike warped black holes in the three dimensional
general massive gravity model, which contains both the gravitational
Chern-Simons term and the linear combination of curvature squared terms
characterizing the new massive gravity besides the Einstein-Hilbert term. The
parameters of the metric are found by solving a quartic equation constrained by
an inequality that imposes the absence of closed timelike curves. Explicit
expressions for the central charges are suggested by exploiting the fact that
these black holes are discrete quotients of spacelike warped AdS(3) and a known
formula for the entropy. Previous results obtained separately in topological
massive gravity and in new massive gravity are recovered as special cases.Comment: 38 pages, 7 figures. v2: minor changes, added refs and an appendix on
self-dual and null z-warped black hole
Entanglement entropy of black holes
The entanglement entropy is a fundamental quantity which characterizes the
correlations between sub-systems in a larger quantum-mechanical system. For two
sub-systems separated by a surface the entanglement entropy is proportional to
the area of the surface and depends on the UV cutoff which regulates the
short-distance correlations. The geometrical nature of the entanglement entropy
calculation is particularly intriguing when applied to black holes when the
entangling surface is the black hole horizon. I review a variety of aspects of
this calculation: the useful mathematical tools such as the geometry of spaces
with conical singularities and the heat kernel method, the UV divergences in
the entropy and their renormalization, the logarithmic terms in the
entanglement entropy in 4 and 6 dimensions and their relation to the conformal
anomalies. The focus in the review is on the systematic use of the conical
singularity method. The relations to other known approaches such as 't Hooft's
brick wall model and the Euclidean path integral in the optical metric are
discussed in detail. The puzzling behavior of the entanglement entropy due to
fields which non-minimally couple to gravity is emphasized. The holographic
description of the entanglement entropy of the black hole horizon is
illustrated on the two- and four-dimensional examples. Finally, I examine the
possibility to interpret the Bekenstein-Hawking entropy entirely as the
entanglement entropy.Comment: 89 pages; an invited review to be published in Living Reviews in
Relativit
Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
We evaluate the one loop determinant of matter multiplet fields of N=4
supergravity in the near horizon geometry of quarter BPS black holes, and use
it to calculate logarithmic corrections to the entropy of these black holes
using the quantum entropy function formalism. We show that even though
individual fields give non-vanishing logarithmic contribution to the entropy,
the net contribution from all the fields in the matter multiplet vanishes. Thus
logarithmic corrections to the entropy of quarter BPS black holes, if present,
must be independent of the number of matter multiplet fields in the theory.
This is consistent with the microscopic results. During our analysis we also
determine the complete spectrum of small fluctuations of matter multiplet
fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references adde
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