Horizon Hair of Extremal Black Holes and Measurements at Null Infinity

Angelopoulos, Yannis; Aretakis, Stefanos; Gajic, Dejan

doi:10.1103/physrevlett.121.131102

Cited by 40 publications

(50 citation statements)

References 64 publications

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“…The physical properties of the thermal bath are modelled by the way we impose boundary conditions, and we shall describe various different well-motivated choices leading to infinite-dimensional near horizon symmetries. We prove that they generically span soft hair excitations in the sense of Hawking, Perry and Strominger [76] (see also [77][78][79][80][81][82][83][84][85]). While our methods are general, we focus on Einstein gravity (possibly with cosmological constant).…”

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confidence: 75%

Spacetime Structure near Generic Horizons and Soft Hair

et al. 2020

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We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. 2. The near horizon algebra of a set of boundary conditions, labeled by a parameter s, is given by the semi-direct sum of diffeomorphisms at the horizon with "spin-s supertranslations". For s = 1 we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. 3. For another choice, we find a non-linear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows to recover the aforementioned (linear) ones as composites. 4. These examples allow to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.

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confidence: 75%

Spacetime Structure near Generic Horizons and Soft Hair

et al. 2020

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“…The proof is a straightforward application of the definitions of H σ,ρ 0 , H σ,ρ 0 , and H σ,1,ρ 0 . We use that the factor (n + 1) 4 appearing in the infinite sums in the definition of || • || H σ,ρ 0 implies control over similar infinite sums with one additional ρ + or ρ c derivative, but no factor (n + 1) 4 . This allows us to conclude that not only m ∈ H σ,ρ 0 , but in fact m ∈ H σ,1,ρ 0 .…”

Section: Gevrey Regularity and Hilbert Spacesmentioning

confidence: 99%

“…In fact, early heuristic and numerical analysis of the linearized problem initiated by Price [44,59,69] suggested that one can do no better than proving inverse polynomial decay estimates, because at sufficiently late times, the leading-order behaviour should be exactly inverse polynomial (this is sometimes referred to as "Price's law"). The presence of so-called polynomial tails in the context of the linear wave equation on asymptotically flat, spherically symmetric black hole backgrounds has recently been proved in a mathematically rigorous setting [4][5][6], where it has moreover been connected to the existence of conservation laws along null hypersurfaces, first discovered by Newman and Penrose at null infinity [65] and discovered in a different guise by Aretakis at the event horizons of extremal black holes 3 [10][11][12][13]. 4 In Fourier space, polynomial tails can alternatively be related to the precise behaviour of resolvent operators corresponding to the wave equation near the zero time frequency, see [48,59,75].…”

Section: Introductionmentioning

confidence: 99%

Quasinormal Modes in Extremal Reissner–Nordström Spacetimes

Gajic

Warnick

2021

Commun. Math. Phys.

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We present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that $$L^2$$ L 2 -based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce $$L^2$$ L 2 -based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting.

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“…Precise late-time asymptotics were derived in [ 5 ]. These asymptotics led to a novel observational signature of ERN [ 4 ] where it was shown that the horizon instability of ERN is in fact “observable” by observers at null infinity. For a detailed study of this signature we refer to the recent [ 15 ].…”

Section: Introductionmentioning

confidence: 99%

A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström

Angelopoulos

Aretakis

Gajic

2020

Commun. Math. Phys.

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It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the backwards direction. In this paper, we construct a definitive (bijective) non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström backgrounds. We make use of physical-space energy norms which are non-degenerate both at the event horizon and at null infinity. As an application of our theory we present a construction of a large class of smooth, exponentially decaying modes. We also derive scattering results in the black hole interior region.

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Horizon Hair of Extremal Black Holes and Measurements at Null Infinity

Cited by 40 publications

References 64 publications

Spacetime Structure near Generic Horizons and Soft Hair

Spacetime Structure near Generic Horizons and Soft Hair

Quasinormal Modes in Extremal Reissner–Nordström Spacetimes

A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström

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