"Nonlinear Evolution of the AdS_4 Black Hole Bomb" Paul Chesler Black Hole Initiative
Abstract: Energy may be extracted from rotating black holes via scattering involving superradiant modes. It was suggested some time ago that if such modes could be confined using a mirror, then an amplification process can occur, converting a significant fraction of the black hole mass into radiation, leading to a so-called "black hole bomb." Anti-de Sitter spacetime contain a natural mirror - the timelike boundary of the geometry - and provides a tractable arena to study the nonlinear evolution of the black hole bomb. Via numerically solving the full 3+1 dimensional Einstein equations, I will present evidence that the AdS black hole bomb is a multistage process. Specifically, via superradiant gravitational modes, Kerr-AdS black holes transition to hairy black holes with a single Killing vector, which then experiences secondary weaker superradiant instabilities.
Peter Hintz University of California, Berkeley
Abstract: I will explain the point of view adopted in a number of recent works, joint with Andras Vasy, in which we prove the global non-linear stability of Minkowski space and of Kerr-(Newman-)de Sitter black holes. Instead of constructing and controlling the non-linear solution incrementally in time, we use a Newton-type iteration scheme: at each iteration step we solve a linearized equation globally. I will in particular address how this informs the choice of gauges, and highlight the crucial role played by constraint damping, first introduced as a tool in numerical relativity by Gundlach et al.