Noether Current, Black Hole Entropy and Spacetime Torsion

TL;DR

This paper demonstrates that spacetime torsion does not influence black hole entropy, as the entropy remains solely dependent on horizon area, despite the presence of torsion in the gravitational theory.

Contribution

It proves that torsion does not affect black hole entropy and clarifies the role of surface and bulk degrees of freedom in torsion-inclusive gravity theories.

Findings

Torsion does not contribute to black hole entropy.

Surface degrees of freedom originate from horizon area.

First law remains unaffected by torsion.

Abstract

We show that the presence of spacetime torsion, unlike any other non-trivial modifications of the Einstein gravity, does \emph{not} affect black hole entropy. The theory being diffeomorphism invariant leads to a Noether current and hence to a Noether charge, which can be associated to the heat content of the spacetime. Furthermore, the evolution of the spacetime inheriting torsion can be encoded in the difference between suitably defined surface and bulk degrees of freedom. For static spacetimes the surface and bulk degrees of freedom coincides, leading to holographic equipartition. In doing so one can see that the surface degrees of freedom originate from horizon area and it is clear that spacetime torsion never contributes to the surface degrees of freedom and hence neither to the black hole entropy. We further show that the gravitational Hamiltonian in presence of torsion does not inherit any torsion dependence in the boundary term and hence the first law originating from the variation of the Hamiltonian, relates entropy to area. This reconfirms our claim that torsion does not modify the black hole entropy.