Thermodynamic Behavior of Time-Dependent Wormholes in Palatini $f(R)$ Gravity

TL;DR

This paper explores the thermodynamic properties of evolving wormholes within Palatini $f(R)$ gravity, deriving field equations, redefining energy conditions, and testing the generalized second law of thermodynamics at different horizons.

Contribution

It provides a novel analysis of thermodynamics in time-dependent wormholes in Palatini $f(R)$ gravity, including entropy variation and horizon-based GSL validity.

Findings

Total entropy variation is derived for evolving wormholes.

The generalized second law holds at apparent horizons under certain conditions.

The thermodynamic behavior depends on the horizon radius and $f(R)$ model parameters.

Abstract

In the frame work of Palatini approach to modified $f(R)$ theories of gravity, we attempt to investigate the thermodynamic behavior of time-dependent wormhole geometries. By considering an evolving wormhole spacetime, we find the field equations in Palatini $f(R)$ gravity. The energy density and pressure are redefined in order to satisfy the continuity equation. To discuss the thermodynamic behavior, an expression for the variation of total entropy is obtained. Then, we extend our discussions to apparent and event horizons of evolving wormholes. We employ the radius of apparent and event horizons to determine the validity of generalized second law (GSL) of thermodynamics which states that the variation of total entropy is non-negative.