Thermodynamics of Apparent Horizon in Brane World Scenarios

TL;DR

This paper derives explicit entropy expressions for the apparent horizon in various brane world models using thermodynamic relations, demonstrating the universality of horizon thermodynamics in these scenarios.

Contribution

It extends the thermodynamic analysis of apparent horizons to brane world models, including RSII, warped DGP, and Gauss-Bonnet cases, providing explicit entropy formulas.

Findings

Explicit entropy expressions for apparent horizons in brane models.

Validation of thermodynamic relations like $dE=TdS + WdV$ in these scenarios.

Applicability to models with Gauss-Bonnet and intrinsic curvature terms.

Abstract

Applying the Clausius relation, $\delta Q=TdS$, to the apparent horizon of FRW universe in brane world scenarios, we show that an explicit entropy expression associated with the apparent horizon can be obtained. On the apparent horizon, the relation, $dE=TdS +WdV$, also holds in the brane world scenarios. We show these results in the RSII model, warped DGP model and the more general case with a Gauss-Bonnet term in the bulk and an intrinsic curvature term on the brane.