Greens Function for Anti de Sitter Gravity

TL;DR

This paper derives the retarded Green's function for linearized gravity in anti de Sitter space, considering boundary conditions where signals are absorbed at infinity, and confirms it reproduces known solutions like the AdS-Schwarzschild metric.

Contribution

It provides an explicit calculation of the retarded Green's function in AdS space with a specific boundary condition, advancing understanding of gravitational perturbations in this background.

Findings

Green's function depends on boundary conditions at infinity

Calculated Green's function reproduces AdS-Schwarzschild solution

Supports the choice of absorbing boundary conditions in AdS

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.