2012/06/30 by Stefanos Aretakis
Physics and Astronomy · Mathematics · #gr-qc #math.AP #math.DG
published as Advances in Theoretical and Mathematical Physics 19 (2015), 507-530 · 18 pages, 5 figures
arxiv created 2013/03/12 · arxiv updated 2021/02/26
We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This result holds in particular for extremal Kerr-Newman and Majumdar-Papapetrou spacetimes and is in stark contrast with the subextremal case for which decay is known for all derivatives along the event horizon.