Linearized Gravity in Brane Backgrounds

TL;DR

This paper analyzes linearized gravity in the Randall-Sundrum brane-world model, deriving the graviton propagator, examining its behavior at various distances, and exploring implications for black hole shapes and connections to AdS/CFT correspondence.

Contribution

It provides an explicit integral expression for the graviton propagator in the Randall-Sundrum background and analyzes its asymptotic behavior and physical implications.

Findings

Graviton propagator reduces to 4D form at long distances

Gravitational fields decay exponentially off the brane

Black holes on the brane are pancake-shaped in extra dimensions

Abstract

A treatment of linearized gravity is given in the Randall-Sundrum background. The graviton propagator is found in terms of the scalar propagator, for which an explicit integral expression is provided. This reduces to the four-dimensional propagator at long distances along the brane, and provides estimates of subleading corrections. Asymptotics of the propagator off the brane yields exponential falloff of gravitational fields due to matter on the brane. This implies that black holes bound to the brane have a "pancake"-like shape in the extra dimension, and indicates validity of a perturbative treatment off the brane. Some connections with the AdS/CFT correspondence are described.