Pseudospectrum of de Sitter black holes

Destounis, Kyriakos; Boyanov, Valentin; Panosso Macedo, Rodrigo

doi:10.1103/PhysRevD.109.044023

Pseudospectrum of de Sitter black holes

Dec 18, 2023

15 pages

Published in:

Phys.Rev.D 109 (2024) 4, 044023

Published: Feb 9, 2024

e-Print:

2312.11630 [gr-qc]

DOI:

10.1103/PhysRevD.109.044023 (publication)

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Abstract: (APS)

Pseudospectral analyses have broadened our understanding of ringdown waveforms from binary remnants by providing insight into both the stability of their characteristic frequencies under environmental perturbations, as well as the underlying transient and nonmodal phenomenology that a mode analysis may miss. In this work, we present the pseudospectrum of scalar perturbations on spherically symmetric black holes in de Sitter spacetimes. We expand upon previous analyses in this setting by calculating the pseudospectrum of Reissner-Nordström-de Sitter black holes and revisit results regarding the stability of quasinormal modes under perturbations in several cases. Of particular note is the case of scalar quasinormal modes with angular parameter

ℓ = 0

, which possess a zero mode related to the presence of a cosmological horizon. We show that the nontrivial eigenfunction associated to this mode has a vanishing energy norm, which poses a challenge in quantifying the magnitude of external perturbations to the wave equation’s potential, as well as in calculating the pseudospectrum. Nonetheless, we present results that suggest that the spectral instability manifestation of

ℓ = 0

scalar quasinormal modes is qualitatively the same as in other cases, in contrast to recent claims. We also analyze the stability of the fundamental mode for

ℓ \geq 1

, finding it to be spectrally stable, except for certain configurations in which a perturbation leads to a discontinuous overtaking of the fundamental unperturbed purely-imaginary mode by a perturbed complex quasinormal mode.

Note:

15 pages, 8 figures, accepted for publication in PRD

References(79)

Figures(8)

[1]

Tests of General Relativity with GWTC-3

Collaborations

•

R. Abbott
(
- LIGO Lab., Caltech
)

et al.

e-Print:
- 2112.06861

[2]

Quasinormal modes of stars and black holes

- Living Rev.Rel. 2 (1999) 2
•
e-Print:
- gr-qc/9909058
•
DOI:
- 10.12942/lrr-1999-2

[3]

TOPICAL REVIEW: Quasinormal modes: the characteristic `sound' of black holes and neutron stars

Hans-Peter Nollert
(
- Tubingen U.
)

- Class.Quant.Grav. 16 (1999) R159-R216
•
DOI:
- 10.1088/0264-9381/16/12/201

[4]

Quasinormal modes of black holes and black branes

Emanuele Berti
(
- Caltech and
- Mississippi U.
)
,
Vitor Cardoso
(
- Lisbon, CENTRA and
- Mississippi U.
)
,
Andrei O. Starinets
(
- Oxford U.
)

- Class.Quant.Grav. 26 (2009) 163001
•
e-Print:
- 0905.2975
•
DOI:
- 10.1088/0264-9381/26/16/163001

[5]

Quasinormal modes of black holes: From astrophysics to string theory

R.A. Konoplya
(
- Tubingen U. and
- Kyoto U.
)
,
A. Zhidenko
(
- ABC Federal U. and
- Sao Paulo U.
)

- Rev.Mod.Phys. 83 (2011) 793-836
•
e-Print:
- 1102.4014
•
DOI:
- 10.1103/RevModPhys.83.793

[6]

Spectral decomposition of the perturbation response of the Schwarzschild geometry

Edward W. Leaver
(
- Utah U.
)

- Phys.Rev.D 34 (1986) 384-408
•
DOI:
- 10.1103/PhysRevD.34.384

[7]

Late time behavior of stellar collapse and explosions: 1. Linearized perturbations

- Phys.Rev.D 49 (1994) 883-889
•
e-Print:
- gr-qc/9307009
•
DOI:
- 10.1103/PhysRevD.49.883

[8]

A Proof of Price's law for the collapse of a selfgravitating scalar field

Mihalis Dafermos
(
- Cambridge U.
)
,
Igor Rodnianski
(
- Princeton U.
)

- Invent.Math. 162 (2005) 381-457
•
e-Print:
- gr-qc/0309115
•
DOI:
- 10.1007/s00222-005-0450-3

[9]

A Sharp Version of Price’s Law for Wave Decay on Asymptotically Flat Spacetimes

Peter Hintz

- Commun.Math.Phys. 389 (2022) 1, 491-542
•
e-Print:
- 2004.01664
•
DOI:
- 10.1007/s00220-021-04276-8

[10]

The non-linear stability of the Schwarzschild family of black holes

Mihalis Dafermos
(
- Princeton U., Math. Dept. and
- Cambridge U., DAMTP
)
,
Gustav Holzegel
(
- Imperial Coll., London and
- Munster U.
)
,
Igor Rodnianski
(
- Princeton U., Math. Dept.
)
,
Martin Taylor
(
- Imperial Coll., London
)

e-Print:
- 2104.08222

[11]

The Cosmological constant

Sean M. Carroll
(
- Chicago U., EFI
)

- Living Rev.Rel. 4 (2001) 1
•
e-Print:
- astro-ph/0004075
•
DOI:
- 10.12942/lrr-2001-1

[12]

Observational evidence from supernovae for an accelerating universe and a cosmological constant

et al.

- Astron.J. 116 (1998) 1009-1038
•
e-Print:
- astro-ph/9805201
•
DOI:
- 10.1086/300499

[13]

Measurements of $\Omega$ and $\Lambda$ from 42 High Redshift Supernovae

Supernova Cosmology Project

Collaboration

•

S. Perlmutter
(
- UC, Berkeley, CfPA
)

et al.

- Astrophys.J. 517 (1999) 565-586
•
e-Print:
- astro-ph/9812133
•
DOI:
- 10.1086/307221

[14]

Final results from the Hubble Space Telescope key project to measure the Hubble constant

HST

Collaboration

•

W.L. Freedman

et al.

- Astrophys.J. 553 (2001) 47-72
•
e-Print:
- astro-ph/0012376
•
DOI:
- 10.1086/320638

[15]

Telling tails in the presence of a cosmological constant

Patrick R. Brady
(
- Caltech
)
,
Chris M. Chambers
(
- Montana State U.
)
,
William Krivan
(
- Tubingen U. and
- Penn State U.
)
,
Pablo Laguna
(
- Penn State U.
)

- Phys.Rev.D 55 (1997) 7538-7545
•
e-Print:
- gr-qc/9611056
•
DOI:
- 10.1103/PhysRevD.55.7538

[16]

Field propagation in de Sitter black holes

- Phys.Rev.D 69 (2004) 104013
•
e-Print:
- gr-qc/0309079
•
DOI:
- 10.1103/PhysRevD.69.104013

[17]

The Wave equation on Schwarzschild-de Sitter spacetimes

e-Print:
- 0709.2766

[18]

The global non-linear stability of the Kerr-de Sitter family of black holes.

- Acta Math. 220 (2018) 1, 1-206,
- Acta Mat. 220 (2018) 1, 1-206,
- Acta Mathematica, 220:1-206, 2018
•
e-Print:
- 1606.04014
•
DOI:
- 10.4310/ACTA.2018.v220.n1.a1