Gravitational entropy of Kerr black holes

TL;DR

This paper evaluates two proposed scalar-based estimators for gravitational entropy in Kerr black holes, finding that one aligns poorly with known entropy values while the other performs better, highlighting the challenges in defining gravitational entropy.

Contribution

The study compares two scalar-based estimators of gravitational entropy in Kerr spacetime, demonstrating that the Rudjord-Grøn-Hervik approach better captures expected black hole entropy.

Findings

Clifton et al.'s estimator does not match Bekenstein-Hawking entropy.

The Rudjord-Grøn-Hervik approach aligns more closely with expected black hole entropy.

The paper highlights difficulties in defining gravitational entropy using scalar invariants.

Abstract

Classical invariants of General Relativity can be used to approximate the entropy of the gravitational field. In this work, we study two proposed estimators based on scalars constructed out from the Weyl tensor, in Kerr spacetime. In order to evaluate Clifton, Ellis and Tavakol's proposal, we calculate the gravitational energy density, gravitational temperature, and gravitational entropy of the Kerr spacetime. We find that in the frame we consider, Clifton et al.'s estimator does not reproduce the Bekenstein-Hawking entropy of a Kerr black hole. The results are compared with previous estimates obtained by the authors using the Rudjord-Gr$\varnothing$n-Hervik approach. We conclude that the latter represents better the expected behaviour of the gravitational entropy of black holes.