Black hole entropy from Poisson brackets: Demystification of some calculations

Recently it has been suggested by 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 based on the Regge-Teitelboim approach is unsatisfactory. The functionals used are really “nondifferentiable” under required variations and also the standard Poisson brackets for these functionals are exactly zero and therefore are 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 brackets. This new Poisson brackets differ from the standard ones in surface terms only and allow us to work with “nondifferentiable” functionals.