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

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.