Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld

TL;DR

This paper explores the fundamental link between thermodynamics and gravity within a braneworld model incorporating curvature corrections, deriving the Friedmann equations from thermodynamic principles and analyzing horizon entropy in Gauss-Bonnet gravity.

Contribution

It demonstrates that Friedmann equations in a Gauss-Bonnet braneworld can be derived from the first law of thermodynamics, revealing a deep connection between gravity and thermodynamics.

Findings

Friedmann equations can be expressed as the first law of thermodynamics.

The entropy of the apparent horizon is derived in Gauss-Bonnet gravity.

Thermodynamical properties of black hole horizons are studied in this framework.

Abstract

We disclose the deep connection between the thermodynamics and gravity in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. We show that the Friedmann equations on the 3-brane embedded in the 5D spacetime with curvature correction terms can be written directly in the form of the first law of thermodynamics on the apparent horizon. Using the first law, we extract the entropy expression of the apparent horizon on the brane, which is useful in studying the thermodynamical properties of the black hole horizon on the brane in Gauss-Bonnet gravity.