Horizon instability of extremal black holes

Aretakis, Stefanos

doi:10.4310/atmp.2015.v19.n3.a1

Cited by 163 publications

(250 citation statements)

References 30 publications

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“…In [4] he showed moreover that, under the assumption of pointwise decay of solutions and their tangential derivatives along the event horizon in affine time v, second-order transversal derivatives even blow up as v → ∞. This blow-up phenomenon has been dubbed the "Aretakis instability" in the literature [33].…”

Section: Previous Results For the Linear Wave Equation On Black Hole mentioning

confidence: 99%

“…Dafermos showed that black hole solutions approaching a subextremal ReissnerNordström solution along the event horizon 4 have a non-empty Cauchy horizon, beyond which the metric can be extended as a C 0 function. Moreover, under a lower bound assumption on the decay of the scalar field along the event horizon, transversal derivatives of φ and the L 2 loc norm of the Christoffel symbols of the metric blow up at the Cauchy horizon.…”

Section: Results For the Spherically Symmetric Einstein-maxwell-scalamentioning

confidence: 99%

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Linear Waves in the Interior of Extremal Black Holes I

Gajic

2016

Commun. Math. Phys.

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Abstract:We consider solutions to the linear wave equation in the interior region of extremal Reissner-Nordström black holes. We show that, under suitable assumptions on the initial data, the solutions can be extended continuously beyond the Cauchy horizon and, moreover, that their local energy is finite. This result is in contrast with previously established results for subextremal Reissner-Nordström black holes, where the local energy was shown to generically blow up at the Cauchy horizon.

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Section: Previous Results For the Linear Wave Equation On Black Hole mentioning

confidence: 99%

Section: Results For the Spherically Symmetric Einstein-maxwell-scalamentioning

confidence: 99%

Linear Waves in the Interior of Extremal Black Holes I

Gajic

2016

Commun. Math. Phys.

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“…In [4], he, moreover, proved the existence of conserved quantities, the Aretakis constants, along H + for solutions φ (that need not be axisymmetric). If non-vanishing, these constants constitute an obstruction to the decay of either φ itself or its transversal derivative.…”

Section: Linear Waves In the Exterior Region Of Extremal Kerrmentioning

confidence: 99%

“…In [22] the construction of r * from [32] is used to extend the local doublenull coordinates in M int to obtain a smooth, global Eddington-Finkelsteintype double-null foliation of M int ∩ {r > e 2 2M }, 4 such that the 2-surfaces S 2 u ,v = {u = u } ∩ {v = v } are diffeomorphic to 2-spheres and we, moreover, obtain quantitative bounds on the metric components in double-null coordinates (see Sect. 2.3).…”

Section: Double-null Coordinatesmentioning

confidence: 99%

Linear Waves in the Interior of Extremal Black Holes II

Gajic

2017

Ann. Henri Poincaré

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Abstract.We consider solutions to the linear wave equation in the interior region of extremal Kerr black holes. We show that axisymmetric solutions can be extended continuously beyond the Cauchy horizon and, moreover, that if we assume suitably fast polynomial decay in time along the event horizon, their local energy is finite. We also extend these results to nonaxisymmetric solutions on slowly rotating extremal Kerr-Newman black holes. These results are the analogues of results obtained in Gajic (Commun Math Phys 353(2), 717-770, 2017) for extremal Reissner-Nordström and stand in stark contrast to previously established results for the subextremal case, where the local energy was shown to generically blow up at the Cauchy horizon.

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“…[43]) if the NE family is a charged version of the zero-damping modes discussed recently in the context of rotating Kerr BHs [45]. It is also unclear if there is any relation between such long lived modes and the instability of exactly extremal geometries [46,47].…”

Section: Physical Review Letters 120 031103 (2018)mentioning

confidence: 99%

A Possible Failure of Determinism in General Relativity

Reall

2018

Physics

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The fate of Cauchy horizons, such as those found inside charged black holes, is intrinsically connected to the decay of small perturbations exterior to the event horizon. As such, the validity of the strong cosmic censorship (SCC) conjecture is tied to how effectively the exterior damps fluctuations. Here, we study massless scalar fields in the exterior of Reissner-Nordström-de Sitter black holes. Their decay rates are governed by quasinormal modes of the black hole. We identify three families of modes in these spacetimes: one directly linked to the photon sphere, well described by standard WKB-type tools; another family whose existence and time scale is closely related to the de Sitter horizon; finally, a third family which dominates for near-extremally charged black holes and which is also present in asymptotically flat spacetimes. The last two families of modes seem to have gone unnoticed in the literature. We give a detailed description of linear scalar perturbations of such black holes, and conjecture that SCC is violated in the near extremal regime.

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Horizon instability of extremal black holes

Cited by 163 publications

References 30 publications

Linear Waves in the Interior of Extremal Black Holes I

Linear Waves in the Interior of Extremal Black Holes I

Linear Waves in the Interior of Extremal Black Holes II

A Possible Failure of Determinism in General Relativity

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