Nonlinear radiation gauge for near Kerr spacetimes

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 [DOI:10.1103/PhysRevD.11.2042] on the Kerr background. It has been shown by Price, Shankar and Whiting [arXiv:gr-qc/0611070] that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In [arXiv:1903.03859], 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.

38 pages. Section 5 rewritten. To appear in Communications in Mathematical Physics

References in corpus (7)

• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• On the Existence of Radiation Gauges in Petrov type II spacetimes
• Local energy estimate on Kerr black hole backgrounds
• A space-time integral estimate for a large data semi-linear wave equation on the Schwarzschild manifold
• The non-linear stability of the Schwarzschild family of black holes
• Kerr stability for small angular momentum
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Cited by in corpus (5)

• Spin-2 Green's Functions on Kerr in Radiation Gauge
• Rotation in vacuum and scalar background: are there alternatives to Newman-Janis algorithm?
• Looking through the Kerr disk
• Perturbations of Kerr with approximate Killing spinors -- Wave version
• Sharp decay for Teukolsky equation in Kerr spacetimes