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Abstract <p>We present a brief review of known analytic results for quasinormal modes (QNMs) of black holes and related space-times. We consider regimes in which the perturbation equations admit exact or perturbative solutions, providing insights complementary to numerical or semi-analytic approaches. We discuss solvable cases in lower-dimensional space-times, algebraically special modes, and exact results in higher-curvature gravity theories. Particular attention is given to the eikonal mode and its correspondence with null geodesics, as well as to beyond-eikonal approximations based on inverse multipole expansions &#xa0;in parametrized metrics. We review analytic solutions obtained in the near-extremal limit of Schwarzschild–de Sitter black holes, in the regime of large field mass, and in pure de Sitter and anti–de Sitter space-times, where boundary conditions play a crucial role. Being not exhaustive, this overview highlights the diversity of techniques and physical insights made possible by analytic treatments of quasinormal spectra.</p>

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Review of Analytic Results on Quasinormal Modes of Black Holes

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Sergei V. Bolokhov,
  • Milena Skvortsova

摘要

Abstract

We present a brief review of known analytic results for quasinormal modes (QNMs) of black holes and related space-times. We consider regimes in which the perturbation equations admit exact or perturbative solutions, providing insights complementary to numerical or semi-analytic approaches. We discuss solvable cases in lower-dimensional space-times, algebraically special modes, and exact results in higher-curvature gravity theories. Particular attention is given to the eikonal mode and its correspondence with null geodesics, as well as to beyond-eikonal approximations based on inverse multipole expansions  in parametrized metrics. We review analytic solutions obtained in the near-extremal limit of Schwarzschild–de Sitter black holes, in the regime of large field mass, and in pure de Sitter and anti–de Sitter space-times, where boundary conditions play a crucial role. Being not exhaustive, this overview highlights the diversity of techniques and physical insights made possible by analytic treatments of quasinormal spectra.