Greens Function for Anti de Sitter Gravity

Abstract

We solve for the retarded Greens function for linearized gravity in a background with a negative cosmological constant, anti de Sitter space. In this background, it is possible for a signal to reach spatial infinity in a finite time. Therefore the form of the Greens function depends on a choice of boundary condition at spatial infinity. We take as our condition that a signal which reaches infinity should be lost, not reflected back. We calculate the Greens function associated with this condition, and show that it reproduces the correct classical solution for a point mass at the origin, the anti de Sitter-Schwarzchild solution.