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Non-linear Stability of Kerr-de Sitter space times

Banff International Research Station for Mathematical Innovation and Discovery

In joint work with András Vasy, we prove the stability of the Kerr-de Sitter family of black holes in the context of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta but without any symmetry assumptions on the initial data. I will describe the general framework which enables us to deal systematically with the diffeomorphism invariance of Einstein's equations, and thus how our solution scheme finds a suitable (wave map type) gauge within a carefully chosen finite-dimensional family of gauges. In particular, I will explain our microlocal proof of a key ingredient of this framework, called `constraint damping,' a device first introduced in numerical relativity.

Mathematics; Geometry; Partial differential equations; Differential geometry

video/mp4

Author affiliation: University of California, Berkeley

2017-06-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61931

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/