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  • Open Access

New method for exact results on quasinormal modes of black holes

Davide Fioravanti* and Daniele Gregori†,‡

  • *Contact author: fioravanti@bo.infn.it
  • †Contact author: daniele.gregori6@unibo.it
  • ‡Also visiting Nordita.
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Phys. Rev. D 112, 125020 – Published 17 December, 2025

DOI: https://doi.org/10.1103/b8pl-vdwy

Abstract

We develop a new method for writing simple exact equations characterizing gravity solutions among which are black holes and in particular quasinormal modes. More precisely, we derive the full system of functional and thermodynamic Bethe ansatz nonlinear integral equations of quantum integrability. In particular, we prove that the quasinormal modes verify different equivalent exact quantization conditions and identify them with Bethe roots. We numerically solve the integral equation and compare the results with other methods. Eventually, we can definitely certify its simplicity, accuracy, and effectiveness. Furthermore, this method connects different unexpected fields and paves the way for innovative ways of investigations in gravity and gauge theories.

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Phys. Rev. D 112, 125020– Published 17 December, 2025
  • Received 28 February 2025
  • Accepted 27 October 2025
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