Routing (electronic design automation)

Quantum mechanics

Mathematical physics

Gauge (firearms)

Einstein

Rotating black hole

Archaeology

Computer science

Classical mechanics

Computer network

Diffeomorphism

Routing protocol

Cosmological constant

Physics

Mathematics

Angular momentum

Link-state routing protocol

Mathematical analysis

Geometry

Anti-de Sitter space

Symmetry (geometry)

Black hole (networking)

De Sitter universe

Universe

History

Acta Mathematica

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.

The global non-linear stability of the Kerr–de Sitter family of black holes