Pseudospectrum and Black Hole Quasinormal Mode Instability

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymp...

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Autores principales:	José Luis Jaramillo, Rodrigo Panosso Macedo, Lamis Al Sheikh
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/113c2317a1c64352bc01aeb604d57321
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spelling	oai:doaj.org-article:113c2317a1c64352bc01aeb604d573212021-12-02T14:35:42ZPseudospectrum and Black Hole Quasinormal Mode Instability10.1103/PhysRevX.11.0310032160-3308https://doaj.org/article/113c2317a1c64352bc01aeb604d573212021-07-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031003http://doi.org/10.1103/PhysRevX.11.031003https://doaj.org/toc/2160-3308We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)PRVDAQ0556-282110.1103/PhysRevD.53.4397] as an “infrared” effect; (ii) the instability of all overtones under small-scale (“ultraviolet”) perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert’s pioneer work and Nollert and Price’s analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)JMAPAQ0022-248810.1063/1.532698]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.José Luis JaramilloRodrigo Panosso MacedoLamis Al SheikhAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031003 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 José Luis Jaramillo Rodrigo Panosso Macedo Lamis Al Sheikh Pseudospectrum and Black Hole Quasinormal Mode Instability
description	We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)PRVDAQ0556-282110.1103/PhysRevD.53.4397] as an “infrared” effect; (ii) the instability of all overtones under small-scale (“ultraviolet”) perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert’s pioneer work and Nollert and Price’s analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)JMAPAQ0022-248810.1063/1.532698]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.
format	article
author	José Luis Jaramillo Rodrigo Panosso Macedo Lamis Al Sheikh
author_facet	José Luis Jaramillo Rodrigo Panosso Macedo Lamis Al Sheikh
author_sort	José Luis Jaramillo
title	Pseudospectrum and Black Hole Quasinormal Mode Instability
title_short	Pseudospectrum and Black Hole Quasinormal Mode Instability
title_full	Pseudospectrum and Black Hole Quasinormal Mode Instability
title_fullStr	Pseudospectrum and Black Hole Quasinormal Mode Instability
title_full_unstemmed	Pseudospectrum and Black Hole Quasinormal Mode Instability
title_sort	pseudospectrum and black hole quasinormal mode instability
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/113c2317a1c64352bc01aeb604d57321
work_keys_str_mv	AT joseluisjaramillo pseudospectrumandblackholequasinormalmodeinstability AT rodrigopanossomacedo pseudospectrumandblackholequasinormalmodeinstability AT lamisalsheikh pseudospectrumandblackholequasinormalmodeinstability
_version_	1718391054820966400

Pseudospectrum and Black Hole Quasinormal Mode Instability

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