Noether charge and black hole entropy in teleparallel gravity

TL;DR

This paper derives the Noether charge in teleparallel gravity, showing its relation to black hole entropy and demonstrating that the entropy-area law issues in general relativity do not occur in this framework.

Contribution

It provides a novel derivation of the Noether charge in teleparallel gravity and links it to black hole entropy without the conformal issues present in general relativity.

Findings

Noether charge yields ADM mass in teleparallel gravity

Black hole entropy can be derived from the Noether charge

Entropy expression is a volume integral, avoiding conformal issues

Abstract

The Noether charge associated to diffeomorphism invariance in teleparallel gravity is derived. It is shown that the latter yields the ADM mass of an asymptotically flat spacetime. The black hole entropy is then investigated based on Wald's prescription that relies on the Noether charge. It is shown that, like in general relativity, the surface gravity can be factored out from such a charge. Consequently, the similarity with the first law of thermodynamics implied by such an approach in general relativity does show up also in teleparallel gravity. It is found that, based on the expression of the first law of black hole mechanics, which is preserved in teleparallel gravity, entropy can thus be extracted from such a Noether charge. The resulting entropy can very naturally be expressed as a {\it volume integral}, though. As such, it is shown that the conformal issue that plagues the entropy-area law within general relativity does not arise in teleparallel gravity based on Wald's approach. The physics behind these features is discussed.