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
- 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
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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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