Non-linear Stability of the Kerr–Newman–de Sitter Family of Charged Black Holes

We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein–Maxwell equations: if one perturbs the initial data of a slowly rotating Kerr–Newman–de Sitter (KNdS) bl...

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Veröffentlicht in:Annals of PDE 2018-06, Vol.4 (1), p.11, Article 11
1. Verfasser: Hintz, Peter
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein–Maxwell equations: if one perturbs the initial data of a slowly rotating Kerr–Newman–de Sitter (KNdS) black hole, then in a neighborhood of the exterior region of the black hole, the metric and the electromagnetic field decay exponentially fast to their values for a possibly different member of the KNdS family. This is a continuation of recent work of the author with Vasy on the stability of the Kerr–de Sitter family for the Einstein vacuum equations. Our non-linear iteration scheme automatically finds the final black hole parameters as well as the gauge in which the global solution exists; we work in a generalized wave coordinate/Lorenz gauge, with gauge source functions lying in a suitable finite-dimensional space. We include a self-contained proof of the linear mode stability of Reissner–Nordström–de Sitter black holes, building on work by Kodama–Ishibashi. In the course of our non-linear stability argument, we also obtain the first proof of the linear (mode) stability of slowly rotating KNdS black holes using robust perturbative techniques.
ISSN:2524-5317
2199-2576
DOI:10.1007/s40818-018-0047-y