Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes

Holzegel, Gustav; Smulevici, Jacques

doi:10.2140/apde.2014.7.1057

Cited by 74 publications

(147 citation statements)

References 56 publications

(164 reference statements)

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“…Energy-decay results of the above form have also been obtained for spacetimes with stable trapping, but the function g(t) decays very slowly. For AdS black holes [21], and also for ultracompact neutron stars [22], results of the form (4.50) have been proved with g(t) = log(2 + t) −2 . Moreover, in both of these examples, this result is sharp in the sense…”

Section: Lower Bound On Decay Ratementioning

confidence: 97%

“…Quasimodes are approximate solutions of the wave equation, with exponentially small error [21,22]. Quasimodes can be used to study local features of potentials, and establish rigorous lower bounds on the uniform decay of fields.…”

Section: B Quasimode Constructionmentioning

confidence: 99%

“…Quasimodes can be used to study local features of potentials, and establish rigorous lower bounds on the uniform decay of fields. Even though one can envisage such a construction for generic backgrounds, it has only been firmly established for backgrounds that admit separable solutions [21,22]. In such cases, the equations of motion governing how certain perturbations propagate on such backgrounds, become a set of coupled ordinary differential equations, for which potentials can be defined.…”

Section: B Quasimode Constructionmentioning

confidence: 99%

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Instability of supersymmetric microstate geometries

Eperon

Reall

Santos

2016

J. High Energ. Phys.

191

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Abstract:We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.

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Section: Lower Bound On Decay Ratementioning

confidence: 97%

Section: B Quasimode Constructionmentioning

confidence: 99%

Section: B Quasimode Constructionmentioning

confidence: 99%

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Instability of supersymmetric microstate geometries

Eperon

Reall

Santos

2016

J. High Energ. Phys.

191

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“…We choose to regard equations (18), (23) and (27) as constraints on the initial data; we will then show that they are preserved by the evolution. Therefore, we solve equations (19)−(22) and (24)−(26) only, with initial data satisfying appropriate restrictions.…”

Section: Existence Of Solution Of the First Order Systemmentioning

confidence: 99%

On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion

Costa

Girão

Natário

et al. 2014

Class. Quantum Grav.

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This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the EinsteinMaxwell-scalar field system with a cosmological constant Λ, with the data on the outgoing initial null hypersurface given by a subextremal ReissnerNordström black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development (MGHD) as a "suitably regular" Lorentzian manifold.In this first part we establish well posedness of the Einstein equations for characteristic data satisfying the minimal regularity conditions leading to classical solutions. We also identify the appropriate notion of maximal solution, from which the construction of the corresponding MGHD follows, and determine breakdown criteria. This is the unavoidable starting point of the analysis; our main results will depend on the detailed understanding of these fundamentals.In the second part of this series [12] we study the stability of the radius function at the Cauchy horizon. In the third and final paper [13] we show that, depending on the decay rate of the initial data, mass inflation may or may not occur; in fact, it is even possible to have (non-isometric) extensions of the spacetime across the Cauchy horizon as classical solutions of the Einstein equations.

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“…To achieve it, we use both an analytical matching scheme as well as a numerical method to explore the * mengjie.wang@ua.pt † herdeiro@ua.pt 1 For recent studies of Maxwell perturbations on pure AdS, see, e.g., [9,10].…”

Section: Introductionmentioning

confidence: 99%

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

Wang

Herdeiro

2016

Phys. Rev. D

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Scalar and gravitational perturbations on Kerr-anti-de Sitter (Kerr-AdS) black holes have been addressed in the literature and have been shown to exhibit a rich phenomenology. In this paper, we complete the analysis of bosonic fields on this background by studying Maxwell perturbations, focusing on superradiant instabilities and vector clouds. For this purpose, we solve the Teukolsky equations numerically, imposing the boundary conditions we have proposed in [1] for the radial Teukolsky equation. As found therein, two Robin boundary conditions can be imposed for Maxwell fields on Kerr-AdS black holes, one of which produces a new set of quasinormal modes even for Schwarzschild-AdS black holes. Here, we show these different boundary conditions produce two different sets of superradiant modes. Interestingly, the "new modes" may be unstable in a larger parameter space. We then study stationary Maxwell clouds that exist at the threshold of the superradiant instability, with the two Robin boundary conditions. These clouds, obtained at the linear level, indicate the existence of a new family of black hole solutions at the nonlinear level, within the Einstein-Maxwell-AdS system, branching off from the KerrNewman-AdS family. As a comparison with the Maxwell clouds, scalar clouds on Kerr-AdS black holes are also studied, and it is shown there are Kerr-AdS black holes that are stable against scalar, but not vector, modes with the same "quantum numbers".

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Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes

Cited by 74 publications

References 56 publications

Instability of supersymmetric microstate geometries

Instability of supersymmetric microstate geometries

On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

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