Thermodynamics of Black Holes in Rastall Gravity

TL;DR

This paper explores the thermodynamic behavior of black holes within Rastall gravity, revealing how matter sources influence thermodynamic properties and identifying a stability threshold related to black hole size.

Contribution

It provides the first detailed analysis of black hole thermodynamics in Rastall gravity, highlighting effects of the Rastall parameter and stability conditions.

Findings

Matter sources amplify effects of Rastall parameter on thermodynamics

Black holes smaller than a critical radius have negative heat capacity

Stable black holes exist only above a certain horizon radius

Abstract

A promising theory in modifying general relativity by violating the ordinary energy-momentum conservation law in curved spacetime is the Rastall theory of gravity. In this theory, geometry and matter fields are coupled to each other in a non-minimal way. Here, we study thermodynamic properties of some black hole solutions in this framework, and compare our results with those of general relativity. We demonstrate how the presence of these matter sources may amplify effects caused by the Rastall parameter in thermodynamic quantities. Our investigation also shows that black holes with radius smaller than a certain amount ($\equiv r_0$) have negative heat capacity in the Rastall framework. In fact, it is a lower bound for the possible values of horizon radius satisfied by stable black holes.