Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula

TL;DR

This paper derives the statistical entropy of stationary dilaton black holes using the Cardy formula, showing agreement with Bekenstein-Hawking entropy under specific conditions and analyzing quantum corrections.

Contribution

It constructs a Virasoro algebra at the horizon for dilaton black holes and examines the entropy including quantum corrections, highlighting differences from previous results.

Findings

Entropy matches Bekenstein-Hawking entropy when period T equals Euclidean periodicity.

Quantum correction introduces a logarithmic term with a -1/2 factor.

Discrepancy in correction factors applies broadly to black holes with similar central charge forms.

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