Linearized Gravity about a Brane

TL;DR

This paper investigates how gravity behaves on a brane embedded in anti-de Sitter space, showing that four-dimensional Newtonian gravity emerges at large distances and can be maintained even with large AdS lengths when scalar curvature terms are included.

Contribution

It demonstrates that four-dimensional gravity can be recovered on a brane with large AdS lengths by including scalar curvature in the brane action, extending previous models.

Findings

Newton's law emerges at large distances compared to AdS lengths

Scalar curvature terms enable four-dimensional gravity with large AdS lengths

Model accommodates AdS lengths larger than experimental bounds

Abstract

We use the Israel condition to treat carefully the weak-field perturbations due to the presence of matter on a 3-brane embedded between two regions of anti-de Sitter (AdS) space with different curvature lengths. A four dimensional Newton's Law only emerges at distances that are large compared to the AdS lengths. When a scalar curvature is included in the brane action, however, it is possible to generate a four dimensional theory of gravity even when one or both of the AdS lengths is large compared to distances along the brane. In particular, we provide an example in which the AdS lengths can be larger than the millimeter experimental bound.