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General Relativity and Quantum Cosmology, gr-qc,Mathematics, Analysis of PDEs, math.AP,
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 IRG/ORG are consistent gauges for the linearized
vacuum Einstein equation on Petrov type II backgrounds. In [arXiv:1903.03859]
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.
