| Abstract: |
| Based on joint work with Peter Hintz and partly with Oliver Petersen, I will discuss the nonlinear stability of Kerr–de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Building on our unconditional earlier stability work for slowly rotating Kerr-de Sitter black holes, the first part concerns the conditional stability of a neighborhood of the black hole exterior (more precisely, the domain of outer communication) in the subextremal range of black hole parameters, namely stability under the assumption of mode stability for the linearized Einstein equation, which I will explain. The second part discusses the stability of the expanding (cosmological) region in a modification of a generalized harmonic gauge introduced by Ringström; in a different type of gauge such a result was obtained recently by Fournodavlos and Schlue. Due to the hyperbolic character of the gauge, the stability result is local near points on the conformal boundary. I will also discuss the smoothness of the metric up to the future conformal boundary, with a Fefferman–Graham type asymptotic expansion, as a consequence of the stability proof. |
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