Statistical Entropy of a Stationary Dilaton Black Hole from Cardy Formula

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 − 2 , which is different from Kaul and Majumdar’s one, −32 . 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 = AH 8πG 2π κT . PACS numbers: 04.70.Dy, 04.62.+V, 97.60.Lf. Typeset using REVTEX ∗email: [email protected] †email: [email protected]