Gauge Invariant Perturbations of the Schwarzschild Spacetime

TL;DR

This paper compiles and explains gauge invariant quantities used in perturbations of Schwarzschild spacetime, building on prior work and focusing on Detweiler's EZ gauge for gravitational self-force analysis.

Contribution

It provides a detailed compilation and explanation of gauge invariant quantities in Schwarzschild perturbations, especially those used by Detweiler, with no prior comprehensive manuscript.

Findings

List of gauge invariant quantities used by Detweiler

Explanation of how Detweiler derived these quantities

Compilation of perturbation results without existing manuscript

Abstract

Beginning with the pioneering work of Regge and Wheeler (Phys. Rev. 108, 1957), there have been many studies of perturbations away from the Schwarzschild spacetime background. In particular several authors (e.g. Moncrief, Ann. Phys 88, 1974) have investigated gauge invariant quantities of the Regge-Wheeler (RW) gauge. Steven Detweiler also investigated perturbations of Schwarzschild in his own gauge, which he denoted the "easy (EZ) gauge", and which he was in the process of adapting for use in the second-order self-force problem. We present here a compilation of some of his working results, arising from notes for which there seems to have been no manuscript in preparation. In particular, we list the gauge invariant quantities used by Detweiler, as well as explain the process by which he found them.