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arXiv · 2507.16493

Transients in black hole perturbation theory

Jérémy Besson·Javier Carballo·Christiana Pantelidou·Benjamin Withers
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Abstract

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.

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Jérémy Besson, Javier Carballo, Christiana Pantelidou, Benjamin Withers. 2025-07-22. Transients in black hole perturbation theory. https://doi.org/10.3389/fphy.2025.1638583

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