Boundedness and Decay for the Teukolsky Equation on Kerr Spacetimes I: The Case $$|a|\ll M$$

Dafermos, Mihalis; Holzegel, Gustav; Rodnianski, Igor

doi:10.1007/s40818-018-0058-8

Cited by 77 publications

(127 citation statements)

References 85 publications

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“…This can be heuristically understood as follows. For purely imaginary frequencies, the solution (15) has an exponential behavior in r, and as such, both the solution and its derivative do not vanish at a given r. However, for certain values of ζ, it is possible that a linear combination of the solution and its derivative vanishes, satisfying (16). Analogous results were observed in Ref.…”

Section: Far Region R − R + ≫ Msupporting

confidence: 79%

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Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions

Ferreira

Herdeiro

2018

Phys. Rev. D

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It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a Bañados-Teitelboim-Zanelli (BTZ) black hole (BH) [1]. To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirrorlike cavity or in anti-de Sitter (AdS) space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/ AdS space is an isolated system and include, as a particular case, the commonly considered Dirichlet boundary conditions (DBCs). Whereas the superradiant modes for some RBCs differ only mildly from the ones with DBCs, in both cases, we find that as we vary the RBCs the imaginary part of the frequency may attain arbitrarily large positive values. We interpret this growth as being sourced by a bulk instability of both confined geometries when certain RBCs are imposed to either the mirrorlike cavity or the AdS boundary, rather than by energy extraction from the BH, in analogy with the BTZ behavior.

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Section: Far Region R − R + ≫ Msupporting

confidence: 79%

“…[9] and further developed in Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23]; (2) imposing the field is confined in a cavity around the BH, via a trapping boundary condition, which was the initial BH bomb proposal [3] and further developed in Refs. [24][25][26];…”

Section: Introductionmentioning

confidence: 99%

Superradiant instabilities in the Kerr-mirror and Kerr-AdS black holes with Robin boundary conditions

Ferreira

Herdeiro

2018

Phys. Rev. D

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“…Penrose: Σ is a Cauchy surface for J − (I + ) , making it globally hyperbolic. 59 [39] plus a detailed study of the geodesics shows that Kruskal space-time is metrically inextendible. 60 59 Alternatively: any incomplete future inextendible timelike curve must crash in the upper r = 0 singularity.…”

Section: Examplesmentioning

confidence: 99%

“…59 [39] plus a detailed study of the geodesics shows that Kruskal space-time is metrically inextendible. 60 59 Alternatively: any incomplete future inextendible timelike curve must crash in the upper r = 0 singularity. Hence I − ( ) lies partly in region II, which is disjoint from J − (I + ) , so that I − ( ) ⊈ J − (x) for all x ∈ J − (I + ).…”

Section: Examplesmentioning

confidence: 99%

Singularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose

Landsman

2021

Found Phys

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In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space–time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the pde literature. As a compromise, one might say that in “generic” or “physically reasonable” space–times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an “Appendix” by Erik Curiel reviews the early history of the definition of a black hole.

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“…Moreover, these extreme curvature components are gauge invariant, hence as a beginning step, one can treat them using TME without imposing any gauge choice. Energy and decay estimates for these extreme curvature components are shown in [34,94] for slowly rotating Kerr backgrounds (|a|/M≪1) by applying a suitable modification of Chandrasekhar's transformations [20]. Based on these estimates, the authors in [2] derived strong decay estimates for TME and obtained a linear stability result of slowly rotating Kerr metrics in an outgoing radiation gauge.…”

Section: General Relativitymentioning

confidence: 99%