On the Existence of Radiation Gauges in Petrov type II spacetimes

TL;DR

This paper investigates the conditions under which radiation gauges, specifically the IRG/ORG, can be imposed in Petrov type II and D spacetimes, including Schwarzschild, to aid metric reconstruction in general relativity.

Contribution

It establishes a new condition on the stress-energy tensor component that allows the full IRG/ORG to be imposed in Petrov type II and D backgrounds, expanding the applicability of radiation gauges.

Findings

Full IRG/ORG can be imposed in Petrov type II and D spacetimes.

A specific condition on the stress-energy tensor enables gauge imposition.

Imposition of IRG demonstrated explicitly in Schwarzschild background.

Abstract

The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be over-specified. Their specification consists of five conditions: four, which we treat here as valid gauge conditions, plus an additional condition on the trace of the metric perturbation. In this work, we utilize a newly developed form of the perturbed Einstein equations to establish a condition -- on a particular tetrad component of the stress-energy tensor -- under which the full IRG/ORG can be imposed. Using gauge freedom, we are able to impose the full IRG for Petrov type II and type D backgrounds, using a different tetrad for each case. As a specific example, we work through the process of imposing the IRG in a Schwarzschild background, using a more traditional approach. Implications for metric reconstruction using the Teukolsky curvature perturbations in type D spacetimes are briefly discussed.