Nonlinear radiation gauge for near Kerr spacetimes. (English) Zbl 1512.83003
Summary: 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 P. L. Chrzanowski in his work on metric reconstruction [Phys. Rev. D (3)11, No. 8, 2042–2062 (1975; doi:10.1103/PhysRevD.11.2042)] on the Kerr background. It has been shown by PL. R. Price et al. [Classical Quantum Gravity 24, No. 9, 2367–2388 (2007; Zbl 1115.83014)] that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In [L. Andersson et al., “Stability for linearized gravity on the Kerr spacetime”, Preprint, 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.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 37F50 | Small divisors, rotation domains and linearization in holomorphic dynamics |
| 83C57 | Black holes |
Citations:
Zbl 1115.83014Software:
xActReferences:
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