Deformations of GR and BH thermodynamics

TL;DR

This paper explores how deformations of General Relativity in four dimensions affect black hole thermodynamics, revealing that black hole entropy remains proportional to the horizon area measured by a specific two-form, matching GR only in the undeformed case.

Contribution

It introduces a formulation of deformed GR theories using SO(3) connections and auxiliary matrices, analyzing their impact on black hole entropy calculations.

Findings

Black hole entropy equals one quarter of the horizon area measured by the two-form MF.

In deformed theories, the entropy measurement differs from the metric-based horizon area.

The entropy formula reduces to the standard GR result in the undeformed limit.

Abstract

In four space-time dimensions General Relativity can be non-trivially deformed. Deformed theories continue to describe two propagating degrees of freedom, as GR. We study Euclidean black hole thermodynamics in these deformations. We use the recently developed formulation that works with SO(3) connections as well as certain matrices M of auxiliary fields. We show that the black hole entropy is given by one quarter of the horizon area as measured by the Lie algebra valued two-form MF, where F is the connection curvature. This coincides with the horizon area as measured by the metric only for the case of General Relativity.