Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory

Hooman Moradpour,Ines G Salako

doi:10.1155/2016/3492796

Abstract

The restrictions on the Rastall theory due to application of 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.

Highlights

For the first time, Jacobson could use thermodynamics to derive the Einstein field equations [1]
In order to study the mutual relation between gravity and thermodynamics, we need a proper energy definition, and it seems that the generalization of the Misner-Sharp mass in various theories is a suitable candidate for this aim [3,4,5,6,7,8,9,10]
It is shown that, in various gravitational theory, if the gravitational field equations are considered as the first law of thermodynamics, we can find an expression for the horizon entropy in the spherically symmetric static spacetimes [7,8,9,10]

Summary

Introduction

Jacobson could use thermodynamics to derive the Einstein field equations [1]. It is shown that, in various gravitational theory, if the gravitational field equations are considered as the first law of thermodynamics, we can find an expression for the horizon entropy in the spherically symmetric static spacetimes [7,8,9,10]. This approach is used to investigate the mutual relation between the gravitational field equations and the system thermodynamic properties, such as entropy, in various gravitational theories [11,12,13,14,15,16,17,18,19,20,21,22,23].

Rastall Field Equations and the Misner-Sharp Mass

Horizon Entropy

Concluding Remarks