Newton's law on an Einstein "Gauss-Bonnet" brane

TL;DR

This paper derives the corrections to Newton's law of gravity on a brane in anti-de Sitter space within Einstein and Einstein-Gauss-Bonnet theories, showing that Gauss-Bonnet terms improve the approximation to Newtonian gravity.

Contribution

It provides analytic expressions for gravitational potential corrections in both theories, demonstrating that Gauss-Bonnet terms lead to smaller deviations from Newton's law across all distances.

Findings

In Einstein theory, the transition from 1/r to 1/r^2 behavior is slow.

In Einstein-Gauss-Bonnet theory, corrections to Newton's potential are small for all r.

Gauss-Bonnet terms improve the approximation to Newtonian gravity on the brane.

Abstract

It is known that Newton's law of gravity holds asymptotically on a flat "brane" embedded in an anti-de Sitter "bulk" ; this was shown not only when gravity in the bulk is described by Einstein's theory but also in Einstein "Lanczos Lovelock Gauss-Bonnet"'s theory. We give here the expressions for the corrections to Newton's potential in both theories, in analytic form and valid for all distances. We find that in Einstein's theory the transition from the 1/r behaviour at small r to the 1/r^2 one at large r is quite slow. In the Einstein Gauss-Bonnet case on the other hand, we find that the correction to Newton's potential can be small for all r. Hence, Einstein Gauss-Bonnet equations in the bulk (rather than simply Einstein's) induce on the brane a better approximation to Newton's law.