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MINI REVIEW article

Front. Phys.
Sec. Interdisciplinary Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1490016
This article is part of the Research Topic Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach View all 6 articles

Quasinormal modes and the analytical continuation of non-self-adjoint operators

Provisionally accepted
Martin G. Richarte Martin G. Richarte 1,2Júlio C. Fabris Júlio C. Fabris 2Alberto Saa Alberto Saa 3*
  • 1 Department of Physics, University of Buenos Aires, Buenos Aires, Buenos Aires, Argentina
  • 2 Department of Physics, Federal University of Espirito Santo, Vitória, Espirito Santo, Brazil
  • 3 Department of Applied Mathematics, State University of Campinas, Campinas, Brazil

The final, formatted version of the article will be published soon.

    We briefly review the analytical continuation method for determining quasinormal modes (QNMs) and the associated frequencies in open systems. We explore two exactly solvable cases based on the Pöschl-Teller potential to show that the analytical continuation method cannot determine the full set of QNMs and frequencies of a given problem starting from the associated bound state problem in Quantum Mechanics. The root of the problem is that many QNMs are the analytically continued counterparts of solutions that do not belong to the domain where the associated Schrödinger operator is self-adjoint, challenging the application of the method for determining full sets of QNMs. We illustrate these problems through the physically relevant case of BTZ black holes, where the natural domain of the problem is the negative real line.

    Keywords: Self-adjoint extensions, Schrödinger operator, quasinormal modes (QNMs), black hole, General relativity (GR)

    Received: 02 Sep 2024; Accepted: 23 Sep 2024.

    Copyright: © 2024 Richarte, Fabris and Saa. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Alberto Saa, Department of Applied Mathematics, State University of Campinas, Campinas, Brazil

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