308 research outputs found
Black hole entropy: statistical mechanics agrees thermodynamics
We discuss the connection between different entropies introduced for black
hole. It is demonstrated on the two-dimensional example that the (quantum)
thermodynamical entropy of a hole coincides (including UV-finite terms) with
its statistical-mechanical entropy calculated according to 't Hooft and
regularized by Pauli-Villars.Comment: 10 pages, latex. Some new discussion added. Version to appear in Phys
Rev.
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.
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
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.
A two-dimensional representation of four-dimensional gravitational waves
The Einstein equation in D dimensions, if restricted to the class of
space-times possessing n = D - 2 commuting hypersurface-orthogonal Killing
vectors, can be equivalently written as metric-dilaton gravity in 2 dimensions
with n scalar fields. For n = 2, this results reduces to the known reduction of
certain 4-dimensional metrics which include gravitational waves. Here, we give
such a representation which leads to a new proof of the Birkhoff theorem for
plane-symmetric space--times, and which leads to an explanation, in which sense
two (spin zero-) scalar fields in 2 dimensions may incorporate the (spin two-)
gravitational waves in 4 dimensions. (This result should not be mixed up with
well--known analogous statements where, however, the 4-dimensional space-time
is supposed to be spherically symmetric, and then, of course, the equivalent
2-dimensional picture cannot mimic any gravitational waves.) Finally, remarks
on hidden symmetries in 2 dimensions are made.Comment: 12 pages, LaTeX, no figures, Int. J. Mod. Phys. D in prin
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
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
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