Gauss-Bonnet gravity, brane world models, and non-minimal coupling

TL;DR

This paper investigates brane world models incorporating a Gauss-Bonnet term and a non-minimally coupled bulk scalar field, deriving static solutions numerically and analyzing their properties.

Contribution

It introduces a new class of brane world solutions with Gauss-Bonnet and non-minimal scalar coupling, providing numerical analysis of static configurations.

Findings

Numerical static solutions are obtained for various parameter values.

The solutions exhibit specific behaviors depending on the coupling and Gauss-Bonnet parameters.

Graphical analysis illustrates the impact of parameters on the brane and bulk geometry.

Abstract

We study the case of brane world models with an additional Gauss-Bonnet term in the presence of a bulk scalar field which interacts non-minimally with gravity, via a possible interaction term of the form $-1/2 \xi R \phi^2$. The Einstein equations and the junction conditions on the brane are formulated, in the case of the bulk scalar field. Static solutions of this model are obtained by solving numerically the Einstein equations with the appropriate boundary conditions on the brane. Finally, we present graphically and comment these solutions for several values of the free parameters of the model.