Thermodynamics of the inhomogeneous perfect fluid LTB model: Modified Bekenstein-Hawking system

TL;DR

This paper explores generalized thermodynamical formulations in the inhomogeneous LTB cosmological model, analyzing conditions under which the first and second laws of thermodynamics hold for different entropy and temperature definitions.

Contribution

It introduces three alternative generalized Bekenstein-Hawking thermodynamic formulations within the LTB model and examines their validity conditions.

Findings

First law holds only for de Sitter case in the first formulation.

Second law requires restrictions on horizon evolution in some cases.

Specific integral forms of parameters are needed for generalized models.

Abstract

The present work deals with three alternative generalized Bekenstein-Hawking formulation of thermodynamical parameters namely entropy and temperature for the universal thermodynamical system bounded by a horizon in the frame work of inhomogeneous perfect fluid Lemaitre-Tolman-Bondi (LTB) model of the Universe. For the first choice, the first law of thermodynamics holds only for the trivial de Sitter case of the LTB model while we need restriction on the evolution of the horizon radius for the validity of the generalized second law of thermodynamics. However, for the other two choices, the first law of thermodynamics holds with some specific (integral) form of the parameters involved but for generalized LTB models.