Black hole entropy from Poisson brackets (demystification of some calculations)

Abstract

Recently it has been suggested by S. Carlip that black hole entropy can be derived from a central charge of the Virasoro algebra arising as a subalgebra in the surface deformations of General Relativity in any dimension. Here it is shown that the argumentation given in Section 2 of hep-th/9812013 and based on the Regge-Teitelboim approach is unsatisfactory. The functionals used are really ``non-differentiable'' under required variations and also the standard Poisson brackets for these functionals are exactly zero so being unable to get any Virasoro algebra with a central charge. Nevertheless Carlip's calculations will be correct if we admit another definition for the Poisson bracket. This new Poisson bracket differs from the standard one in surface terms only and allows to work with ``non-differentiable'' functionals.