Thermodynamic analysis of the static spherically symmetric field equations in Rastall theory

TL;DR

This paper investigates the thermodynamics of static spherically symmetric spacetimes in Rastall gravity, deriving relations for mass, entropy, and work, and comparing them with Einstein gravity to understand Rastall's impact.

Contribution

It introduces a thermodynamic framework for Rastall theory, deriving mass, entropy, and work expressions, and compares these with Einstein gravity results.

Findings

Derived the Misner-Sharp mass in Rastall gravity.

Obtained entropy and work expressions at the horizon.

Compared thermodynamic quantities with Einstein gravity.

Abstract

The restrictions on the Rastall theory due to apply the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.