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arXiv · 1807.03802

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

Yannis Angelopoulos·Stefanos Aretakis·Dejan Gajic
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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.

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Yannis Angelopoulos, Stefanos Aretakis, Dejan Gajic. 2018-07-10. Late-time asymptotics for the wave equation on extremal Reissner-Nordstr\"om backgrounds. https://doi.org/10.1016/j.aim.2020.107363

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