Thermodynamics of Lemaitre-Tolman-Bondi Model

TL;DR

This paper investigates the thermodynamic properties of an inhomogeneous universe modeled by the Lemaitre-Tolman-Bondi solution, demonstrating the connection between Einstein's equations and thermodynamics, and examining the second law at horizons.

Contribution

It establishes the equivalence of Einstein's field equations with the unified first law of thermodynamics in the LTB model and tests the generalized second law at different horizons.

Findings

The trapping horizon coincides with the apparent horizon.

Einstein equations are equivalent to the unified first law of thermodynamics.

The generalized second law holds at the apparent and event horizons.

Abstract

Here we consider our universe as inhomogeneous spherically symmetric Lemaitre-Tolman-Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.