Thermodynamics in Higher Dimensional Vaidya Space-Time

TL;DR

This paper explores thermodynamics in higher-dimensional Vaidya spacetime, deriving entropy variations and examining the generalized second law at different horizons, highlighting conditions under which thermodynamic laws hold.

Contribution

It establishes the equivalence of Einstein's field equations and the unified first law in higher dimensions and analyzes the validity of the GSL at various horizons.

Findings

GSL holds at apparent horizons when using the first law and area law.

GSL does not hold at event horizons in any dimension.

Entropy variation is derived from both the unified first law and Gibbs' law.

Abstract

In this work, we have considered the Vaidya spacetime in null radiating fluid with perfect fluid in higher dimension and have found the solution for barotropic fluid. We have shown that the Einstein's field equations can be obtained from Unified first law i.e., field equations and unified first law are equivalent. The first law of thermodynamics has also been constructed by Unified first law. From this, the variation of entropy function has been derived on the horizon. The variation of entropy function inside the horizon has been derived using Gibb's law of thermodynamics. So the total variation of entropy function has been constructed at apparent and event horizons both. If we do not assume the first law, then the entropy on the both horizons can be considered by area law and the variation of total entropy has been found at both the horizons. Also the validity of generalized second law (GSL) of thermodynamics has been examined at both apparent and event horizons by using the first law and the area law separately. When we use first law of thermodynamics and Bekenstein-Hawking area law of thermodynamics, the GSL for apparent horizon in any dimensions are satisfied, but the GSL for event horizon can not be satisfied in any dimensions.