Dynamics and Thermodynamics of (2+1)-Dimensional Evolving Lorentzian Wormhole

TL;DR

This paper explores the thermodynamic properties of (2+1)-dimensional evolving Lorentzian wormholes, showing how Einstein's equations relate to the first law of thermodynamics at the trapping horizon.

Contribution

It demonstrates the equivalence of Einstein field equations and the first law of thermodynamics for a specific class of evolving wormholes in (2+1) dimensions.

Findings

Einstein equations can be rewritten as a thermodynamic first law at the trapping horizon.

Explicit expressions for energy, temperature, entropy, and work density are derived.

The thermodynamic description applies to particular shape and potential functions.

Abstract

In this paper we study the relationship between the Einstein field equations for the (2+1)-dimensional evolving wormhole and the first law of thermodynamics. It has been shown that the Einstein field equations can be rewritten as a similar form of the first law of thermodynamics at the dynamical trapping horizon (as proposed by Hayward) for the dynamical spacetime which describes intrinsic thermal properties associated with the trapping horizon. For a particular choice of the shape and potential functions we are able to express field equations as a similar form of first law of thermodynamics $dE=-TdS+WdA$ at the trapping horizons. Here $E=\rho A$, $T=-\kappa /2\pi $, $S=4\pi \tilde{r}_{A}$, $W=(\rho -p)/2$%, and $A=\pi \tilde{r}_{A}^{2}$, are the total matter energy, horizon temperature, wormhole entropy, work density and volume of the evolving wormhole respectively.