Covariant Gravitational Equations on Brane World with Gauss-Bonnet term

TL;DR

This paper derives covariant gravitational equations for a brane world with a Gauss-Bonnet term, incorporating bulk effects via Weyl curvature, and applies it to cosmology to obtain a generalized Friedmann equation.

Contribution

It introduces a covariant formalism for brane worlds with Gauss-Bonnet corrections, extending previous models to include bulk effects in a unified way.

Findings

Derived covariant gravitational equations with Gauss-Bonnet term.

Obtained a generalized Friedmann equation for brane cosmology.

Calculated Weyl curvature effects from a black hole solution.

Abstract

We present the covariant gravitational equations to describe a four-dimensional brane world in the case with the Gauss-Bonnet term in a bulk spacetime, assuming that gravity is confined on the $Z_2$ symmetric brane. It contains some components of five-dimensional Weyl curvature ($E_{\mu\nu}$) which describes all effects from the bulk spacetime just as in the case of the Randall-Sundrum second model. Applying this formalism to cosmology, we derive the generalized Friedmann equation and calculate the Weyl curvature term, which is directly obtained from a black hole solution.