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Path to an exact WKB analysis of black hole quasinormal modes

Taiga Miyachi*

Ryo Namba†

Hidetoshi Omiya‡

Naritaka Oshita§

  • RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 351-0198, Japan

  • Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan; The Hakubi Center for Advanced Research, Kyoto University, Yoshida Ushinomiyacho, Sakyo-ku, Kyoto 606-8501, Japan; and RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 351-0198, Japan

  • *Contact author: tmiyachi@omu.ac.jp
  • †Contact author: ryo.namba@riken.jp
  • ‡Contact author: omiya@tap.scphys.kyoto-u.ac.jp
  • §Contact author: naritaka.oshita@yukawa.kyoto-u.ac.jp
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Phys. Rev. D 111, 124045 – Published 24 June, 2025

DOI: https://doi.org/10.1103/1gmr-9f1g

Abstract

We investigate black hole quasinormal modes using the exact Wentzel–Kramers–Brillouin (WKB) method. We perform an analytic continuation from the horizon to infinity along the positive real axis of the radial coordinate and impose appropriate boundary conditions at these asymptotic positions. We clarify the role of previously overlooked logarithmic spirals of Stokes curves and branch cuts emerging from the horizon. We carefully reformulate the derivation of the quasinormal mode conditions using the exact WKB analysis, incorporating the contributions from these features into the calculation. We successfully derive correct results for both solvable model examples and the Schwarzschild spacetime. Our formulation enjoys straightforward extensions to other background geometries as well as a wide range of other physical systems.

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Phys. Rev. D 111, 124045– Published 24 June, 2025
  • Received 2 April 2025
  • Accepted 29 May 2025
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