Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons

TL;DR

This paper explores the thermodynamics and dynamics of non-static Lorentzian wormholes with anisotropic pressure, deriving exact solutions and analyzing the validity of the generalized second law at horizons.

Contribution

It provides new exact solutions for evolving Lorentzian wormholes with anisotropic pressure and links Einstein's equations with thermodynamic laws without assuming a specific shape function.

Findings

Einstein's field equations are equivalent to the unified first law for the wormhole.

The first law of thermodynamics is derived for the wormhole model.

The generalized second law of thermodynamics holds at apparent and event horizons.

Abstract

We have investigated the non-static Lorentzian Wormhole model in presence of anisotropic pressure. We have presented some exact solutions of Einstein equations for anisotropic pressure case. Introducing two EoS parameters we have shown that these solutions give very rich dynamics of the universe yielding to the different expansion history of it in the $r$ - direction and in the $T$ - direction. The corresponding explicit forms of the shape function $b(r)$ is presented.We have shown that the Einstein's field equations and unified first law are equivalent for the dynamical wormhole model. The first law of thermodynamics has been derived by using the Unified first law. The physical quantities including surface gravity and the temperature are derived for the wormhole. Here we have obtained all the results without any choice of the shape function. The validity of generalized second law (GSL) of thermodynamics has been examined at apparent and event horizons for the evolving Lorentzian wormhole.