Back Reaction of Gravitational Radiation on the Schwarzschild Black Hole

TL;DR

This paper investigates the back reaction of gravitational waves on Schwarzschild black holes, demonstrating that the Regge-Wheeler gauge can be used to compute the effective energy-momentum tensor at the horizon and infinity, revealing its scalar-field-like behavior.

Contribution

It shows that the Regge-Wheeler gauge is suitable for calculating the effective energy-momentum tensor of gravitational perturbations at the horizon and infinity.

Findings

The effective energy-momentum tensor behaves like a scalar field's stress-energy tensor.

The Regge-Wheeler gauge can be used beyond asymptotically flat regions.

Some metric components diverge, but physical quantities remain well-defined.

Abstract

We address some of the issues that appear in the study of back reaction in Schwarzschild backgrounds. Our main object is the effective energy-momentum tensor (EEMT) of gravitational perturbations. It is commonly held that only asymptotically flat or radiation gauges can be employed for these purposes. We show that the traditional Regge-Wheeler gauge for the perturbations of the Schwarszchild metric can also be used for computing physical quantities both at the horizon and at infinity. In particular, we find that the physically relevant components of the EEMT of gravitational perturbations have the same asymptotic behaviour as the stress-energy tensor of a scalar field in the Schwarzschild background, even though some of the metric components themselves diverge.