Transients in black hole perturbation theory

TL;DR

This paper reviews transient phenomena in black hole perturbation theory, focusing on the non-normal nature of quasinormal modes and their implications for energy localization and growth near black holes.

Contribution

It provides a comprehensive summary of recent developments in understanding transients in black hole perturbations in both frequency and time domains.

Findings

Identification of transient plateaus as long-lived quasinormal mode sums

Observation of transient growth near black hole phase transitions

Analysis of transients in higher-derivative Sobolev norms

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.