Black hole nonmodal linear stability: the Schwarzschild (A)dS cases

G. DOTTI

Nueva York

Conferencia; 21st International Conference on General Relativity and Gravitation; 2016

International Society on General Relativity and Gravitation

The nonmodal linear stability of the Schwarzschild black hole established in Phys.Rev. Lett. 112 (2014) 191101 is generalized to the case of nonnegative cosmologicalconstant. Two gauge invariant combinations (G,H) of perturbed scalars made outof the Weyl tensor and its first covariant derivative are found such that the map[h] (G,H), [h] an equivalence class under gauge transformations of a solution of thelinearized Einstein?s equation, is invertible. For arbitrary perturbations consistentwith the background asymptote, G and H are bounded in the the outer static region.At large times, the perturbation decays to a linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter background solutions. In the case of negative cosmological constant, it is shown that there is a choice of boundary condition at the time-like boundary under which the Schwarzschild anti de Sitter black hole is unstable.This talk is based on arXiv:1603.037493749