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

Abstract

In this paper, we generalize the analysis of the [Formula: see text]-brane via the inclusion of a term proportional to the Gauss–Bonnet invariant. We consider an action of the form [Formula: see text], where [Formula: see text] is the trace of the stress–energy tensor, [Formula: see text] is the Ricci scalar, and [Formula: see text] is a real parameter that controls the contribution of the Gauss–Bonnet invariant [Formula: see text]. We introduce the first-order formalism to obtain solutions for the source field of the brane in the special case where [Formula: see text] and illustrate its procedure with an application to the sine-Gordon model. We also investigate the general case of the [Formula: see text]-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.