Thermodynamics in Quasi-Spherical Szekeres Space-Time

TL;DR

This paper investigates the validity of the generalized second law of thermodynamics in an inhomogeneous, higher-dimensional quasi-spherical Szekeres space-time universe by analyzing apparent horizon thermodynamics through two different methods.

Contribution

It provides a comparative analysis of the GSL validity using both the first law approach and a direct surface gravity method in a complex inhomogeneous cosmological model.

Findings

GSL holds under specific conditions in the model.

Conditions depend on the horizon entropy and internal entropy variations.

The two approaches yield consistent results under certain assumptions.

Abstract

We have considered that the universe is the inhomogeneous $(n+2)$ dimensional quasi-spherical Szekeres space-time model. We consider the universe as a thermodynamical system with the horizon surface as a boundary of the system. To study the generalized second law (GSL) of thermodynamics through the universe, we have assumed the trapped surface is the apparent horizon. Next we have examined the validity of the generalized second law of thermodynamics (GSL) on the apparent horizon by two approaches: (i) using first law of thermodynamics on the apparent horizon and (ii) without using the first law. In the first approach, the horizon entropy have been calculated by the first law. In the second approach, first we have calculated the surface gravity and temperature on the apparent horizon and then horizon entropy have found from area formula. The variation of internal entropy have been found by Gibb's law. Using these two approaches separately, we find the conditions for validity of GSL in $(n+2)$ dimensional quasi-spherical Szekeres model.