On the thin-shell limit of branes in the presence of Gauss-Bonnet interactions

TL;DR

This paper investigates how Gauss-Bonnet interactions affect the thin-shell limit of thick-brane models, revealing that such interactions break the equivalence between matter and geometric configurations seen in Einstein gravity.

Contribution

It demonstrates that Gauss-Bonnet terms prevent the internal structure from simplifying in the thin-shell limit, unlike in Einstein gravity, and compares two families of thick-brane models.

Findings

Gauss-Bonnet interactions break the equivalence between matter and geometric configurations.

In the presence of Gauss-Bonnet terms, shells retain non-trivial internal structure.

Comparison of thick-brane models with and without Gauss-Bonnet terms.

Abstract

In this paper we study thick-shell braneworld models in the presence of a Gauss-Bonnet term. We discuss the peculiarities of the attainment of the thin-shell limit in this case and compare them with the same situation in Einstein gravity. We describe the two simplest families of thick-brane models (parametrized by the shell thickness) one can think of. In the thin-shell limit, one family is characterized by the constancy of its internal density profile (a simple structure for the matter sector) and the other by the constancy of its internal curvature scalar (a simple structure for the geometric sector). We find that these two families are actually equivalent in Einstein gravity and that the presence of the Gauss-Bonnet term breaks this equivalence. In the second case, a shell will always keep some non-trivial internal structure, either on the matter or on the geometric sectors, even in the thin-shell limit.