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MINI REVIEW article

Front. Phys.

Sec. Interdisciplinary Physics

Volume 13 - 2025 | doi: 10.3389/fphy.2025.1638583

This article is part of the Research TopicQuasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary ApproachView all 13 articles

Transients in black hole perturbation theory

Provisionally accepted
Jeremy  BessonJeremy Besson1,2Javier  CarballoJavier Carballo3Christiana  PantelidouChristiana Pantelidou4*Benjamin  WithersBenjamin Withers3*
  • 1Institut de Mathematiques de Bourgogne, Dijon, France
  • 2Max-Planck-Institut fur Gravitationsphysik, Hanover, Germany
  • 3University of Southampton, Southampton, United Kingdom
  • 4University College Dublin, Dublin, Ireland

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

Black hole quasinormal modes arise as eigenmodes of a non-normal Hamiltonian and consequently they do not obey orthogonality relations with respect to commonly used inner products, for example, the energy inner product. A direct consequence of this is the appearance of transient phenomena. This review summarises current developments on the topic, both in frequency-and time-domain. In particular, we discuss the appearance of i) transient plateaus: arbitrarily long-lived sums of quasinormal modes, corresponding to localised energy packets near the future horizon; ii) transient growth, with the latter either appearing in the vicinity of black hole phase transitions or in the context of higher-derivative Sobolev norms.1 Second order QNMs, usually referred to as QQNMs, have also been constructed recently [3,4].

Keywords: Non-modal, quasinormal modes (QNMs), black holes, transients, Pseudospectra, Black hole spectroscopy, Non-normal, Ringdown

Received: 30 May 2025; Accepted: 09 Jul 2025.

Copyright: © 2025 Besson, Carballo, Pantelidou and Withers. 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:
Christiana Pantelidou, University College Dublin, Dublin, Ireland
Benjamin Withers, University of Southampton, Southampton, United Kingdom

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