Nonlinear Radiation Gauge for Near Kerr Spacetimes

Lars Andersson; Thomas Bäckdahl; Pieter Blue; Siyuan Ma

doi:10.1007/s00220-022-04461-3

Nonlinear Radiation Gauge for Near Kerr Spacetimes

Commun Math Phys. 2022;396(1):45-90. doi: 10.1007/s00220-022-04461-3. Epub 2022 Aug 16.

Authors

Lars Andersson¹, Thomas Bäckdahl², Pieter Blue³, Siyuan Ma^{1

4}

Affiliations

¹ Albert Einstein Institute, Am Mühlenberg 1, 14476 Potsdam, Germany.
² Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96 Gothenburg, Sweden.
³ Maxwell Institute and The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD UK.
⁴ Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France.

Abstract

In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by Chrzanowski in his work on metric reconstruction (Chrzanowski in Phys Rev D 11:2042-2062, 1975) on the Kerr background. It has been shown by Price et al. (Class Quantum Gravity 24:2367-2388, 2007) that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In (Andersson et al. Stability for linearized gravity on the Kerr spacetime, 2019), the ORG was used in proving linearized stability for the Kerr spacetime, and the new non-linear radiation gauge introduced here is a direct generalization of that gauge condition, and is intended to be used to study the stability of Kerr black holes under the evolution generated by the vacuum Einstein equation.