On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes

Warnick, Claude

doi:10.1007/s00220-014-2171-1

Cited by 82 publications

(158 citation statements)

References 62 publications

(175 reference statements)

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“…This is due to the presence of stable trapping. Note that this sharpness can also be concluded from later work showing the existence of quasinormal modes converging to the real axis at an exponential rate as the real part of the frequency and angular momentum tend to infinity [64,32]. (For some asymptotically flat five dimensional black holes a similar inverse logarithmic lower bound was shown in [2].…”

Section: Introductionsupporting

confidence: 69%

Uniform Boundedness and Continuity at the Cauchy Horizon for Linear Waves on Reissner–Nordström–AdS Black Holes

Kehle

2019

Commun. Math. Phys.

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Motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS spacetimes, we initiate the study of massive scalar waves satisfying g ψ − µψ = 0 on the interior of Anti-de Sitter (AdS) black holes. We prescribe initial data on a spacelike hypersurface of a Reissner-Nordström-AdS black hole and impose Dirichlet (reflecting) boundary conditions at infinity. It was known previously that such waves only decay at a sharp logarithmic rate (in contrast to a polynomial rate as in the asymptotically flat regime) in the black hole exterior. In view of this slow decay, the question of uniform boundedness in the black hole interior and continuity at the Cauchy horizon has remained up to now open. We answer this question in the affirmative.Conjecture 1 (C 0 formulation of strong cosmic censorship). For generic compact or asymptotically flat (asymptotically Anti-de Sitter) vacuum initial data, the maximal Cauchy development of (EE) is inextendible as a Lorentzian manifold with C 0 (continuous) metric.Surprisingly, the C 0 formulation (Conjecture 1) was recently proved to be false for both cases Λ = 0 and Λ > 0 (see discussion later, [17]). However, the following weaker, yet well-motivated, formulation introduced by Christodoulou in [9] is still expected to hold true (at least) in the asymptotically flat case (Λ = 0).Conjecture 2 (Christodoulou's re-formulation of strong cosmic censorship). For generic asymptotically flat vacuum initial data, the maximal Cauchy development of (EE) is inextendible as a Lorentzian manifold with C 0 (continuous) metric and locally square integrable Christoffel symbols.1 More precisely, this holds true for subextremal and non-trivially rotating(charged) Kerr(Reissner-Nordström) black holes which we will assume for the rest of the paper, unless explicitly stated otherwise.In order to gain insight about SCC, the most naive approach (often referred to as "poor man's linearization") is to study solutions of (1.1) with µ = 0 on a fixed explicit black hole spacetime (e.g. Kerr or Reissner-Nordström). This can be considered as the most naive toy model for (EE) with initial data close to Kerr or Reissner-Nordström data, for which many features of (EE) including the non-linear terms and the tensorial structure are neglected; see the pioneering works for asymptotically flat (Λ = 0) black holes [60,48,49,8]. Under the identification ψ ∼ g and ∂ψ ∼ Γ, where ψ is a solution to (1.1), Conjecture 1 corresponds to a failure of ψ to be continuous (C 0 ) at the Cauchy horizon. Similarly, Conjecture 2 corresponds to a failure of ψ to lie in H 1 loc at the Cauchy horizon. The state of the art for Λ = 0 and Λ > 0. The definitive disproof [17] of Conjecture 1 was preceded by corresponding results on the level of (1.1).Linear level for Λ = 0. In the asymptotically flat case (Λ = 0) it was shown in [26,27] (see also [34]) that solutions of (1.1) with µ = 0 arising from data on a spacelike hypersurface remain continuous and uniformly bounded (no C 0 blow-up) at the Cauchy horizon of general subextremal Kerr or...

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Section: Introductionsupporting

confidence: 69%

Uniform Boundedness and Continuity at the Cauchy Horizon for Linear Waves on Reissner–Nordström–AdS Black Holes

Kehle

2019

Commun. Math. Phys.

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“…(3.12) 8 A related approach to meromorphic continuation, also motivated by the study of Anti-de Sitter black holes, was independently developed by Warnick [269]. It is based on physical space techniques for hyperbolic equations and it also provides meromorphic continuation of resolvents for even asymptotically hyperbolic metrics [269, §7.5].…”

Section: Meromorphic Continuation In Geometric Scatteringmentioning

confidence: 99%

Mathematical study of scattering resonances

2017

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“…The quasinormal frequencies of AdS black holes have direct interpretation in terms of the dual conformal field theory CFT, for details we refer to [14][15][16][17][18][19][20]. The QNMs can be used as a powerful tool to detect the extra dimensions of spacetime, in other words the brane-world scenarios assume the existence of extra dimensions, so that multidimensional black holes can be formed in a laboratory [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Behavior of quasinormal modes and high dimension RN–AdS black hole phase transition

et al. 2016

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In this work we use the quasinormal frequencies of a massless scalar perturbation to probe the phase transition of the high dimension charged AdS black hole. The signature of the critical behavior of this black hole solution is detected in the isobaric as well as in isothermal process. This paper is a natural generalization of Liu et al. (JHEP 1409(JHEP :179, 2014 to higher dimensional spacetime. More precisely our study shows a clear signal for any dimension d in the isobaric process. As to the isothermal case, we find that this signature can be affected by other parameters like the pressure and the horizon radius. We conclude that the quasinormal modes can be an efficient tool to investigate the first-order phase transition, but fail to disclose the signature of the second-order phase transition.

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On Quasinormal Modes of Asymptotically Anti-de Sitter Black Holes

Cited by 82 publications

References 62 publications

Uniform Boundedness and Continuity at the Cauchy Horizon for Linear Waves on Reissner–Nordström–AdS Black Holes

Uniform Boundedness and Continuity at the Cauchy Horizon for Linear Waves on Reissner–Nordström–AdS Black Holes

Mathematical study of scattering resonances

Behavior of quasinormal modes and high dimension RN–AdS black hole phase transition

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