276 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
Non-minimal coupling and quantum entropy of black hole
Formulating the statistical mechanics for a scalar field with non-minimal
coupling in a black hole background we propose modification of
the original 't Hooft ``brick wall'' prescription. Instead of the Dirichlet
condition we suggest some scattering ansatz for the field functions at the
horizon. This modifies the energy spectrum of the system and allows one to
obtain the statistical entropy dependent on the non-minimal coupling. For
the entropy renormalizes the classical Bekenstein-Hawking entropy in
the correct way and agrees with the result previously obtained within the
conical singularity approach. For a positive , however, the results
differ.Comment: 16 pages, latex, no figures; an error in calculation of the entropy
corrected, the entropy now is positive for any non-minimal couplin
Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics
Starting from metric of the general nonextreme stationary axisymmetric black
hole in four-dimensional spacetime, both statistical-mechanical and
thermodynamical entropies are studied. First, by means of the "brick wall"
model in which the Dirichlet condition is replaced by a scattering ansatz for
the field functions at the horizon and with Pauli-Villars regularization
scheme, an expression for the statistical-mechanical entropy arising from the
nonminimally coupled scalar fields is obtained. Then, by using the conical
singularity method Mann and Solodukhin's result for the Kerr-Newman black hole
(Phys. Rev. D54, 3932(1996)) is extended to the general stationary black hole
and the nonminimally coupled scalar field. We last shown by comparing the two
results that the statistical-mechanical entropy and one-loop correction to the
thermodynamical entropy are equivalent for coupling . After
renormalization, a relation between the two entropies is given.Comment: 18 pages, Latex, nofigue. Accepted by Phys. Rev.
Quantum entropy of the Kerr black hole arising from gravitational perturbation
The quantum entropy of the Kerr black hole arising from gravitational
perturbation is investigated by using Null tetrad and \'t Hooft\'s brick-wall
model. It is shown that effect of the graviton\'s spins on the subleading
correction is dependent of the square of the spins and the angular momentum per
unit mass of the black hole, and contribution of the logarithmic term to the
entropy will be positive, zero, and negative for different value of .Comment: 8 pages, 1 figure, Latex. to appear in Phys. Rev.
Divergences problem in black hole brick-wall model
In this work we review, in the framework of the so-called brick wall model,
the divergence problem arising in the one loop calculations of various
thermodynamical quantities, like entropy, internal energy and heat capacity.
Particularly we find that, if one imposes that entanglement entropy is equal to
the Bekenstein-Hawking one, the model gives problematic results. Then a
proposal of solution to the divergence problem is made following the zeroth law
of black hole mechanics.Comment: 19 pages, reviseted-extended version accepted by Phys. Rev.
Conical geometry and quantum entropy of a charged Kerr black hole
We apply the method of conical singularities to calculate the tree-level
entropy and its one-loop quantum corrections for a charged Kerr black hole. The
Euclidean geometry for the Kerr-Newman metric is considered. We show that for
an arbitrary periodization in Euclidean space there exists a conical
singularity at the horizon. Its -function like curvatures are
calculated and are shown to behave similar to the static case. The heat kernel
expansion for a scalar field on this conical space background is derived and
the (divergent) quantum correction to the entropy is obtained. It is argued
that these divergences can be removed by renormalization of couplings in the
tree-level gravitational action in a manner similar to that for a static black
hole.Comment: 22 pages, latex, no figures; minor corrections mad
Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
The algebraic approach to black hole quantization requires the horizon area
eigenvalues to be equally spaced. As shown previously, for a neutral
non-rotating black hole, such eigenvalues must be -fold degenerate if
one constructs the black hole stationary states by means of a pair of creation
operators subject to a specific algebra. We show that the algebra of these two
building blocks exhibits symmetry, where the area
operator generates the U(1) symmetry. The three generators of the SU(2)
symmetry represent a {\it global} quantum number (hyperspin) of the black hole,
and we show that this hyperspin must be zero. As a result, the degeneracy of
the -th area eigenvalue is reduced to for large , and
therefore, the logarithmic correction term should be added to the
Bekenstein-Hawking entropy. We also provide a heuristic approach explaining
this result, and an evidence for the existence of {\it two} building blocks.Comment: 15 pages, Revtex, to appear in Phys. Rev.
Non-abelian gauge antisymmetric tensor fields
We construct the theory of non-abelian gauge antisymmetric tensor fields,
which generalize the standard Yang-MIlls fields and abelian gauge p-forms. The
corresponding gauge group acts on the space of inhomogeneous differential forms
and it is shown to be a supergroup. The wide class of generalized Chern-Simons
actions is constructed.Comment: 20 pages, Late
One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
The quantum entanglement entropy of an eternal black hole is studied. We
argue that the relevant Euclidean path integral is taken over fields defined on
-fold covering of the black hole instanton. The statement that
divergences of the entropy are renormalized by renormalization of gravitational
couplings in the effective action is proved for non-minimally coupled scalar
matter. The relationship of entanglement and thermodynamical entropies is
discussed.Comment: 17 pages, latex, no figure
On "Non-Geometric" Contribution To The Entropy Of Black Hole Due To Quantum Corrections
The quantum corrections to the entropy of charged black holes are calculated.
The Reissner-Nordstrem and dilaton black holes are considered. The appearance
of logarithmically divergent terms not proportional to the horizon area is
demonstrated. It is shown that the complete entropy which is sum of classical
Bekenstein-Hawking entropy and the quantum correction is proportional to the
area of quantum-corrected horizon.Comment: Latex, 9 page
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