Thermodynamics of Evolving Lorentzian Wormholes at Apparent Horizon in $f(R)$ Theory of Gravity

TL;DR

This paper investigates the thermodynamic behavior of evolving Lorentzian wormholes within $f(R)$ gravity, revealing modified thermodynamic relations at the apparent horizon compared to Einstein's general relativity.

Contribution

It demonstrates that the thermodynamic laws for evolving wormholes in $f(R)$ gravity include an extra entropy term, extending the understanding of wormhole thermodynamics beyond general relativity.

Findings

Wormholes can be derived from specific $f(R)$ models in radiation backgrounds.

The field equations at the apparent horizon resemble a thermodynamic relation with an additional entropy term.

Thermodynamic relations differ from Einstein gravity by including a $Tdar{S}$ term.

Abstract

In the context of modified $f(R)$ gravity, we attempt to study the thermodynamic properties of the evolving Lorentzian wormholes at the apparent horizon. It is shown that the wormhole can be derived from a particular $f(R)$ model in the radiation background. Moreover, it has been shown that the field equations can be cast to a similar form $dE = TdS + WdV + Td\bar{S}$ at the apparent horizon for the evolving Lorentzian wormhole. Compared to the case of Einstein's general relativity, an additional term $Td\bar{S}$ appears here.