English

Late-time asymptotics for the wave equation on extremal Reissner-Nordstr\"om backgrounds

General Relativity and Quantum Cosmology 2021-02-25 v2 Analysis of PDEs

Abstract

We derive the precise late-time asymptotics for solutions to the wave equation on extremal Reissner-Nordstr\"om 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.

Keywords

Cite

@article{arxiv.1807.03802,
  title  = {Late-time asymptotics for the wave equation on extremal Reissner-Nordstr\"om backgrounds},
  author = {Yannis Angelopoulos and Stefanos Aretakis and Dejan Gajic},
  journal= {arXiv preprint arXiv:1807.03802},
  year   = {2021}
}

Comments

87 pages, 10 figures; version accepted for publication