Conservation equation on braneworlds in six dimensions

TL;DR

This paper investigates six-dimensional braneworld models within Einstein-Gauss-Bonnet gravity, demonstrating conserved brane energy-momentum regardless of bulk matter, highlighting differences from five-dimensional scenarios.

Contribution

It establishes the conservation of brane energy-momentum in six dimensions with Einstein-Gauss-Bonnet gravity, independent of bulk matter, and clarifies the role of the Gauss-Bonnet term.

Findings

Energy-momentum on the brane is always conserved.

The Gauss-Bonnet term is essential for well-posed equations in six dimensions.

Conservation holds regardless of bulk energy-momentum presence.

Abstract

We study braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. The Gauss-Bonnet term is crucial for the equations to be well-posed in six dimensions when non-trivial matter on the brane is included (the also involved induced gravity term is not significant for their structure), and the matching conditions of the braneworld are known. We show that the energy-momentum of the brane is always conserved, independently of any regular bulk energy-momentum tensor, contrary to the situation of the five-dimensional case.