Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon

TL;DR

This paper introduces a generalized Vaidya solution within Lovelock gravity, explores the thermodynamics of the apparent horizon, and derives entropy and energy expressions consistent with existing theories.

Contribution

It extends the Vaidya solution to generic Lovelock gravity and analyzes the thermodynamics of the apparent horizon in this context.

Findings

Derived a generalized entropy expression for the apparent horizon.

Obtained an energy expression matching the generalized Misner-Sharp energy.

Extended previous solutions in Gauss-Bonnet gravity to more general Lovelock gravity.

Abstract

We present a kind of generalized Vaidya solutions in a generic Lovelock gravity. This solution generalizes the simple case in Gauss-Bonnet gravity reported recently by some authors. We study the thermodynamics of apparent horizon in this generalized Vaidya spacetime. Treating those terms except for the Einstein tensor as an effective energy-momentum tensor in the gravitational field equations, and using the unified first law in Einstein gravity theory, we obtain an entropy expression for the apparent horizon. We also obtain an energy expression of this spacetime, which coincides with the generalized Misner-Sharp energy proposed by Maeda and Nozawa in Lovelock gravity.