Thermodynamics in quasi-spherical Szekeres space-time

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 on the apparent horizon by two approaches: i) using the first law of thermodynamics on the apparent horizon and ii) without using the first law. In the first approach, the horizon entropy has 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 the horizon entropy has been found from the area formula. The variation of internal entropy has been found by Gibb's law. Using these two approaches separately, we find the conditions for validity of GSL in the (n+2)-dimensional quasi-spherical Szekeres model.