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Workshop

Stability and instability of asymptotically anti-de Sitter black holes

  • Gustav Holzegel
E1 05 (Leibniz-Saal)

Abstract

I will introduce the problem of black hole stability in the context of a negative cosmological constant, describing some of the geometric and analytic challenges characteristic of this problem. In the second part, I will discuss recent work with Olivier Graf (Grenoble) establishing linear stability of Schwarzschild-anti de Sitter (AdS) black holes to gravitational perturbations. This is the statement that solutions to the linearisation of the Einstein equations $\textrm{Ric} = -\frac{3}{\ell^2} g$ around a Schwarzschild-AdS metric arising from regular initial data and with standard Dirichlet boundary conditions imposed at the conformal boundary (inherited from fixing the conformal class of the non-linear metric) remain globally uniformly bounded on the black hole exterior and in fact decay inverse logarithmically to a linearised Kerr-AdS metric.

Antje Vandenberg

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Alexandra Linde

Augsburg University Contact via Mail

Christian Bär

Potsdam University

Bernhard Hanke

Augsburg University

Anna Wienhard

Max Planck Institute for Mathematics in the Sciences

Burkhard Wilking

University of Münster