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
c
12
=
A
H
8πG
2π
κT
.