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Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula

Jiliang Jing·Mu-Lin Yan
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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 $\frac{c}{12}= \frac{A_H}{8πG}\frac{2π}{κT}$.

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Jiliang Jing, Mu-Lin Yan. 2000-09-27. Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula. https://doi.org/10.1103/physrevd.63.024003

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