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arXiv · 2406.15924

Overdamped QNM for Schwarzschild black holes

Michael Hitrik·Maciej Zworski
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Abstract

We prove that the number of quasinormal modes (QNM) for Schwarzschild and Schwarzschild-de Sitter black holes in a disc of radius $ r $ is bounded from below by $ c r^3 $. This shows that the recent upper bound by J\'ez\'equel is sharp. The argument is an application of a spectral asymptotics result for non-self-adjoint operators which provides a finer description of QNM and explains the emergence of a distorted lattice on which they lie. Our presentation gives a general result about exponentially accurate Bohr-Sommerfeld quantization rules for one dimensional problems. The description of QNM allows their accurate evaluation ``deep in the complex" where numerical methods break down due to pseudospectral effects.

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Michael Hitrik, Maciej Zworski. 2024-06-22. Overdamped QNM for Schwarzschild black holes. https://arxiv.org/abs/2406.15924

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