Comparison of Variations of Statistical and Wald's Entropies

TL;DR

This paper investigates how the statistical entropy of matter fields outside a black hole varies along a Killing vector in generalized gravity theories, using Lie derivatives and energy-momentum tensor identification.

Contribution

It introduces a method to analyze entropy variations in generalized gravity theories using Lie derivatives and energy-momentum tensors.

Findings

Derived expressions for entropy variation in generalized gravity

Applicable to matter fields outside black holes

Provides a framework for entropy analysis in alternative gravity theories

Abstract

We write the variation of the statistical entropy of matter fields outside a black hole along a Killing vector. This is done for generalized theories of gravity, using a Lie derivative and identification of the energy momentum tensor.