Central charges and boundary fields for two-dimensional dilatonic black holes

In this paper we first show that within the Hamiltonian description of general relativity the central charge of a near horizon asymptotic symmetry group is zero, and therefore that the entropy of the system cannot be estimated using Cardy’s formula. This is done by mapping a static black hole to a two-dimensional space. We explain how such a charge can appear only to a static observer who chooses to stay permanently outside the black hole. Then an alternative argument is given for the presence of a universal central charge. Finally, we suggest an effective quantum theory on the horizon that is compatible with the thermodynamic behavior of the black hole.