Covariant description of the black hole entropy in 3D gravity

TL;DR

This paper investigates the entropy of 3D black holes with torsion using a covariant partition function approach, addressing regularization issues and boundary conditions to accurately compute entropy.

Contribution

It introduces a covariant method for calculating black hole entropy in 3D gravity with torsion, clarifying boundary contributions and regularization.

Findings

Correct entropy value obtained with two boundaries

Boundary choice affects entropy interpretation

Regularization aligns with grand canonical conditions

Abstract

We study the entropy of the black hole with torsion using the covariant form of the partition function. The regularization of infinities appearing in the semiclassical calculation is shown to be consistent with the grand canonical boundary conditions. The correct value for the black hole entropy is obtained provided the black hole manifold has two boundaries, one at infinity and one at the horizon. However, one can construct special coordinate systems, in which the entropy is effectively associated with only one of these boundaries.