Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula

Abstract

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 $\frac{c}{12}=\frac{A_H}{8\pi G}\frac{2\pi }{\kappa T}$.

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

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