Horizon Instability of Extremal Black Holes

Aretakis, Stefanos

doi:10.48550/arxiv.1206.6598

Cited by 59 publications

(135 citation statements)

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“…Thus, our result implies the divergent behavior of the covariant derivatives of the fields at the late time. In the study of the Aretakis instability, the conserved quantities on the horizon, called the Aretakis constants, make the analysis easier [9][10][11][12][13][14][15]. In this paper, we also show that Aretakis constants in AdS 2 become some components of the higher-order covariant derivatives of the field in the parallelly propagated frame.…”

Section: Introductionmentioning

confidence: 59%

“…In Refs. [11][12][13][14][15], it has also been shown that the same phenomena occur in other extremal black hole spacetimes and for other fields. Many aspects of the Aretakis instability have been studied in Refs.…”

Section: Introductionmentioning

confidence: 66%

“…Since the AdS 2 structures appear in the vicinity of extremal black hole horizons [8,15,[21][22][23][24][25]29], we expect that the Aretakis instability in extremal black hole spacetimes has a similar geometrical meaning as our result in AdS 2 cases. In fact, this expectation is correct, i.e., the Aretakis instability for black hole cases [9][10][11][12][13][14] can be understood as that some components of the higher-order covariant derivatives of the field in the parallelly propagated frame are unbounded at the late time [38].…”

Section: Summary and Discussionmentioning

confidence: 99%

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Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes

Katagiri,

Kimura

2021

Preprint

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We discuss dynamics of massive Klein-Gordon fields in two-dimensional Anti-de Sitter spacetimes (AdS 2 ), in particular conserved quantities and non-modal instability on the future Poincaré horizon called, respectively, the Aretakis constants and the Aretakis instability. We find out the geometrical meaning of the Aretakis constants and instability in a parallel-transported frame along a null geodesic, i.e., some components of the higher-order covariant derivatives of the field in the paralleltransported frame are constant or unbounded at the late time, respectively. Because AdS 2 is maximally symmetric, any null hypersurfaces have the same geometrical properties. Thus, if we prepare parallel-transported frames along any null hypersurfaces, we can show that the same instability emerges not only on the future Poincaré horizon but also on any null hypersurfaces. This implies that the Aretakis instability in AdS 2 is the result of singular behaviors of the higher-order covariant derivatives of the fields on the whole AdS infinity, rather than a blow-up on a specific null hypersurface. It is also discussed that the Aretakis constants and instability are related to the conformal Killing tensors. We further explicitly demonstrate that the Aretakis constants can be derived from ladder operators constructed from the spacetime conformal symmetry.

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Section: Introductionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 66%

Section: Summary and Discussionmentioning

confidence: 99%

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Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes

Katagiri,

Kimura

2021

Preprint

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“…The absence of unstable modes may be a good enough stability proof for a physicist, but not for a mathematician: mode stability does not imply linear stability. A rigorous proof of linear stability was carried out by Kay and Wald for Schwarzschild BHs [386], but the extension of this analysis to Kerr is still work in progress [387][388][389][390][391], and there is now evidence for instability in extremal Kerr BHs [392] (see also [393][394][395][396]). For our purposes, and with the previous caveats, we will consider the absence of unstable modes as a physically satisfactory stability criterion.…”

Section: Black Holes In General Relativitymentioning

confidence: 99%

Testing General Relativity with Present and Future Astrophysical Observations

Berti,

Barausse,

Cardoso

et al. 2015

Preprint

133

207

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One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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“…(B) The spacetime exhibits an Aretakis-type instability (see [22], [23]), where there are waves arising from smooth, compactly supported initial data, whose local energy 5 fails to decay in a neighbourhood of the ergosurface, although it decays everywhere else. In fact, a nonzero amount of energy is concentrated in a smaller and smaller region, leading to pointwise blow-up.…”

Section: Introductionmentioning

confidence: 99%

Evanescent ergosurface instability

Keir

2020

Analysis & PDE

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Some exotic compact objects, including supersymmetric microstate geometries and certain boson stars, possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event horizon exhibits a linear instability of a peculiar kind: either there are solutions to the linear wave equation which concentrate a finite amount of energy into an arbitrarily small spatial region, or the energy of waves measured by a stationary family of observers can be amplified by an arbitrarily large amount. In certain circumstances we can rule out the first type of instability. We also provide a generalisation to asymptotically Kaluza-Klein manifolds. This instability bears some similarity with the "ergoregion instability" of Friedman [1], and we use many of the results from the recent proof of this instability by Moschidis [2].

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Horizon Instability of Extremal Black Holes

Cited by 59 publications

References 0 publications

Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes

Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes

Testing General Relativity with Present and Future Astrophysical Observations

Evanescent ergosurface instability

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