Scalar-tensor representation to $f(R,T)-$brane with Gauss-Bonnet gravity

TL;DR

This paper extends the analysis of $f(R,T)$-branes by incorporating Gauss-Bonnet gravity, using first-order formalism and scalar-tensor approaches to find solutions and study stability, revealing new behaviors due to the Gauss-Bonnet term.

Contribution

It introduces a generalized $f(R,T)$-brane model with Gauss-Bonnet term and develops first-order and scalar-tensor formalisms for solution finding and stability analysis.

Findings

Gauss-Bonnet term can induce qualitatively different brane behaviors

First-order formalism effectively finds solutions in specific models

Brane stability under tensor perturbations is analyzed

Abstract

In this paper, we generalize the analysis of the $f(R,T)-$brane via the inclusion of a term proportional to the Gauss-Bonnet invariant. We consider an action of the form $F(R,G,T)=f(R,T)+\alpha G$, where $T$ is the trace of the stress-energy tensor, $R$ is the Ricci scalar, and $\alpha$ is a real parameter that controls the contribution of the Gauss-Bonnet invariant $G$. We introduce the first-order formalism to obtain solutions for the source field of the brane in the special case where $f(R,T)=R+\beta T$ and illustrate its procedure with an application to the sine-Gordon model. We also investigate the general case of the $f(R,T)-$brane via the use of the scalar-tensor formalism, where we also use the first-order formalism to obtain solutions. Finally, we investigate the linear stability of the brane under tensor perturbations of the the modified Einstein's field equations. Our results indicate that the Gauss-Bonnet term may induce qualitatively different behaviors of the quantities on the brane, provided that its contribution is large enough.