Jl. Jing et Ml. Yan, Statistical entropy of a stationary dilaton black hole from the Cardy formula - art. no. 024003, PHYS REV D, 6302(2), 2001, pp. 4003
With Carlip's boundary conditions, a standard Virasoro subalgebra with a co
rresponding central charge for a stationary dilaton black hole obtained in
the low-energy effective field theory describing string is constructed at a
Killing horizon. The statistical entropy of a stationary dilaton black hol
e yielded by the standard Cardy formula agrees with its Bekenstein-Hawking
entropy only if we take the period T of function v as the periodicity of th
e Euclidean black hole. On the other hand, if we consider a first-order qua
ntum correction then the entropy contains a logarithmic term with a factor
-1/2, which is different from that of Kaul and Majumdar, -3/2. We also show
that the discrepancy is not just for the dilaton black hole, but for any o
ne whose corresponding central charge takes the form c/12 = (A(H)/8 piG)(2
pi /kT).