Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula

Details Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula

2000-05-24

arxiv.org/abs/gr-qc/0005105v2

Phys.Rev.D63:024003,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, no figure, RevTex. Accepted for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.63.024003

With Carlip's boundary conditions, a standard Virasoro subalgebra with corresponding central charge for stationary dilaton black hole obtained in the low-energy effective field theory describing string is constructed at a Killing horizon. The statistical entropy of stationary dilaton black hole yielded by standard Cardy formula agree with its Bekenstein-Hawking entropy only if we take period $ T$ of function $v$ as the periodicity of the Euclidean black hole. On the other hand, if we consider first-order quantum correction then the entropy contains a logarithmic term with a factor $-{1/2}$, which is different from Kaul and Majumdar's one, $-{3/2}$. We also show that the discrepancy is not just for the dilaton black hole, but for any one whose corresponding central change takes the form $\frac{c}{12}= \frac{A_H}{8\pi G}\frac{2\pi}{\kappa T}$.

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