Transient dynamics of quasinormal mode sums
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910707789856768 |
|---|---|
| author | Carballo, Javier Withers, Benjamin |
| author_facet | Carballo, Javier Withers, Benjamin |
| contents | 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 dS$_{d+1}$ and the BTZ black hole. We also provide numerical examples for scalar perturbations of Schwarzschild-AdS$_{d+1}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transient dynamics of quasinormal mode sums Carballo, Javier Withers, Benjamin High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology Nuclear Theory 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 dS$_{d+1}$ and the BTZ black hole. We also provide numerical examples for scalar perturbations of Schwarzschild-AdS$_{d+1}$, 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. |
| title | Transient dynamics of quasinormal mode sums |
| topic | High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology Nuclear Theory |
| url | https://arxiv.org/abs/2406.06685 |