2016/12/31 by Peter Hintz · 1 citation
Mathematics · Physics and Astronomy · #math.AP #gr-qc #math-ph #math.DG #math.MP #msc:83C57 #msc:83C22 #msc:35B40 #msc:83C35
paper · pdf · doi:10.1007/s40818-018-0047-y
published as Annals of PDE, 4(1):11, Apr 2018 · 112 pages, 8 figures. v2 is the published version, with typos corrected
arxiv created 2020/05/27 · arxiv updated 2020/05/28
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.