Translator Disclaimer
March 2018 The global non-linear stability of the Kerr–de Sitter family of black holes
Peter Hintz, András Vasy
Author Affiliations +
Acta Math. 220(1): 1-206 (March 2018). DOI: 10.4310/ACTA.2018.v220.n1.a1

Abstract

We establish the full global non-linear stability of the Kerr–de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extending the linear and non-linear analysis on black hole spacetimes described in a sequence of earlier papers by the authors: we develop a general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein’s equations. In particular, the iteration scheme used to solve Einstein’s equations automatically finds the parameters of the Kerr–de Sitter black hole that the solution is asymptotic to, the exponentially decaying tail of the solution, and the gauge in which we are able to find the solution; the gauge here is a wave map/DeTurck type gauge, modified by source terms which are treated as unknowns, lying in a suitable finite-dimensional space.

Citation

Download Citation

Peter Hintz. András Vasy. "The global non-linear stability of the Kerr–de Sitter family of black holes." Acta Math. 220 (1) 1 - 206, March 2018. https://doi.org/10.4310/ACTA.2018.v220.n1.a1

Information

Received: 1 July 2016; Published: March 2018
First available in Project Euclid: 19 June 2019

zbMATH: 1391.83061
MathSciNet: MR3816427
Digital Object Identifier: 10.4310/ACTA.2018.v220.n1.a1

Subjects:
Primary: 83C57
Secondary: 35B40, 58J47, 83C05, 83C35

Rights: Copyright © 2018 Institut Mittag-Leffler

JOURNAL ARTICLE
206 PAGES


SHARE
Vol.220 • No. 1 • March 2018
Back to Top