Transient dynamics of quasinormal mode sums
Transient dynamics of quasinormal mode sums
Quasinormal modes of spacetimes with event horizons are typically governed by a non-normal operator. This gives rise to spectral instabilities, a topic of recent interest in the black hole pseudospectrum programme. In this work we show that non-normality leads to the existence of arbitrarily long-lived sums of short-lived quasinormal modes, corresponding to localising packets of energy near the future horizon. There exist sums of M quasinormal modes whose lifetimes scale as log M. This transient behaviour results from large cancellations between non-orthogonal quasinormal modes. We provide simple closed-form examples for a massive scalar field in the static patch of dSd+1 and the BTZ black hole. We also provide numerical examples for scalar perturbations of Schwarzschild-AdSd+1, and gravitational perturbations of Schwarzschild in asymptotically flat spacetime, using hyperboloidal foliations. The existence of these perturbations is linked to certain properties of black hole pseudospectra. We comment on implications for thermalisation times in holographic plasmas.
cond-mat.str-el, gr-qc, hep-th, nucl-th
Carballo, Javier
6c0512bf-c1ae-4e62-9b5e-dfac07d23195
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
Carballo, Javier
6c0512bf-c1ae-4e62-9b5e-dfac07d23195
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
Carballo, Javier and Withers, Benjamin
(2024)
Transient dynamics of quasinormal mode sums.
Journal of High Energy Physics, 2024 (10), [84].
(doi:10.1007/JHEP10(2024)084).
Abstract
Quasinormal modes of spacetimes with event horizons are typically governed by a non-normal operator. This gives rise to spectral instabilities, a topic of recent interest in the black hole pseudospectrum programme. In this work we show that non-normality leads to the existence of arbitrarily long-lived sums of short-lived quasinormal modes, corresponding to localising packets of energy near the future horizon. There exist sums of M quasinormal modes whose lifetimes scale as log M. This transient behaviour results from large cancellations between non-orthogonal quasinormal modes. We provide simple closed-form examples for a massive scalar field in the static patch of dSd+1 and the BTZ black hole. We also provide numerical examples for scalar perturbations of Schwarzschild-AdSd+1, and gravitational perturbations of Schwarzschild in asymptotically flat spacetime, using hyperboloidal foliations. The existence of these perturbations is linked to certain properties of black hole pseudospectra. We comment on implications for thermalisation times in holographic plasmas.
Text
2406.06685v2
- Accepted Manuscript
Text
JHEP10(2024)084
- Version of Record
More information
Accepted/In Press date: 31 August 2024
e-pub ahead of print date: 10 October 2024
Keywords:
cond-mat.str-el, gr-qc, hep-th, nucl-th
Identifiers
Local EPrints ID: 494949
URI: http://eprints.soton.ac.uk/id/eprint/494949
ISSN: 1126-6708
PURE UUID: 954073d1-a95a-4145-9581-39a8daeb49d5
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Date deposited: 23 Oct 2024 17:14
Last modified: 29 Oct 2024 02:27
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Author:
Javier Carballo
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