Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
arXiv:1807.03802 · doi:10.1016/j.aim.2020.107363
Abstract
We derive the precise late-time asymptotics for solutions to the wave equation on extremal Reissner-Nordström black holes and explicitly express the leading-order coefficients in terms of the initial data. Our method is based on purely physical space techniques. We derive novel weighted energy hierarchies and develop a singular time inversion theory, which allow us to uncover the subtle contribution of both the near-horizon and near-infinity regions to the precise asymptotics. We introduce a new horizon charge and provide applications pertaining to the interior dynamics of extremal black holes. Our work confirms, and in some cases extends, the numerical and heuristic analysis of Lucietti-Murata-Reall-Tanahashi, Ori-Sela and Blaksley-Burko.
87 pages, 10 figures; version accepted for publication