Central charges and boundary fields for two dimensional dilatonic black holes

TL;DR

This paper investigates the central charge in two-dimensional dilatonic black holes, showing it is zero in the Hamiltonian framework but proposing an alternative perspective and an effective quantum horizon theory.

Contribution

It demonstrates the vanishing of the central charge in the Hamiltonian description and introduces a new effective quantum theory on the horizon.

Findings

Central charge is zero in Hamiltonian formalism.

A universal central charge can only be observed by a static outside observer.

Proposes an effective quantum horizon theory consistent with black hole thermodynamics.

Abstract

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 only appear 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 thermodynamics behaviour of the black hole.