Einstein gravity on the codimension 2 brane?

TL;DR

This paper derives the effective four-dimensional Einstein equations for braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity, revealing conditions under which standard gravity emerges and discussing corrections related to brane embedding.

Contribution

It provides the general matching conditions for Einstein-Gauss-Bonnet braneworlds, showing that standard Einstein equations are recovered even with non-compact extra dimensions.

Findings

Standard Einstein equations are recovered on the brane.

Additional corrections depend on brane embedding and are not determined by the braneworld alone.

Relaxing regularity conditions introduces possible modifications to gravity.

Abstract

We look at general braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the Einstein-Gauss-Bonnet braneworld, which remarkably turn out to give precisely the four-dimensional Einstein equations for the induced metric and matter on the brane, even when the extra dimensions are non-compact and have infinite volume. We also show that relaxing regularity of the curvature in the vicinity of the brane, or alternatively having a finite width brane, gives rise to an additional possible correction to the Einstein equations, which contains information on the brane's embedding in the bulk and cannot be determined from knowledge of the braneworld alone. We comment on the advantages and disadvantages of each possibility, and the relevance of these results regarding a possible solution of the cosmological constant problem.