Violation of First Law of Thermodynamics in f(R,T) Gravity

TL;DR

This paper demonstrates that the first law of black hole thermodynamics generally does not hold in f(R,T) gravity, revealing violations due to non-local entropy terms, with potential exceptions in special cases.

Contribution

It explicitly derives the entropy expression in f(R,T) gravity and proves the violation of the first law, highlighting the non-local nature of entropy in this theory.

Findings

First law of thermodynamics is violated in general for f(R,T) gravity.

Entropy contains non-local integral terms.

Possible special cases where the first law is recovered.

Abstract

In this Letter, we derived the first law of thermodynamics using the method proposed by Wald. Treating the entropy as Noether charge and comparing with the usual first law of thermodynamics, we obtained the expression of entropy explicitly which contains infinitely many non-local terms (i.e. the integral terms). We have proved, in general, that the first law of black bole thermodynamics is violated for $f(R,T)$ gravity. But there might exist some special cases in which the first law for $f(R,T)$ gravity is recovered.