Extremal black hole horizons

Armas, Jay; Harmark, Troels; Obers, Niels A.

doi:10.1007/jhep03(2018)099

Cited by 24 publications

(3 citation statements)

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“…Besides having proved to be extremely useful in finding new black hole solutions [14][15][16][17][18] in asymptotically flat space, we demonstrate here that the blackfold approach [7,19] is a powerful tool for studying hydrodynamic (i.e. Gregory-Laflamme) and elastic instabilities of higher-dimensional black holes in the ultraspinning regime and away from it.…”

Section: Introductionmentioning

confidence: 74%

“…Additionally, we find a long-lived mode that describes a wiggly time-dependent deformation of a black ring. We comment on disagreements between our results and corresponding ones obtained from a large D analysis of black ring instabilities.Besides having proved to be extremely useful in finding new black hole solutions [14][15][16][17][18] in asymptotically flat space, we demonstrate here that the blackfold approach [7, 19] is a powerful tool for studying hydrodynamic (i.e. Gregory-Laflamme) and elastic instabilities of higher-dimensional black holes in the ultraspinning regime and away from it.…”

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confidence: 99%

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Instabilities of thin black rings: closing the gap

Armas

Parisini

2019

J. High Energ. Phys.

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We initiate the study of dynamical instabilities of higher-dimensional black holes using the blackfold approach, focusing on asymptotically flat boosted black strings and singlyspinning black rings in D ≥ 5. We derive novel analytic expressions for the growth rate of the Gregory-Laflamme instability for boosted black strings and its onset for arbitrary boost parameter. In the case of black rings, we study their stability properties in the region of parameter space that has so far remained inaccessible to numerical approaches. In particular, we show that very thin (ultraspinning) black rings exhibit a Gregory-Laflamme instability, giving strong evidence that black rings are unstable in the entire range of parameter space. For very thin rings, we show that the growth rate of the instability increases with increasing non-axisymmetric mode m while for thicker rings, there is competition between the different modes. However, up to second order in the blackfold approximation, we do not observe an elastic instability, in particular for large modes m 1, where this approximation has higher accuracy. This suggests that the Gregory-Laflamme instability is the dominant instability for very thin black rings. Additionally, we find a long-lived mode that describes a wiggly time-dependent deformation of a black ring. We comment on disagreements between our results and corresponding ones obtained from a large D analysis of black ring instabilities.Besides having proved to be extremely useful in finding new black hole solutions [14][15][16][17][18] in asymptotically flat space, we demonstrate here that the blackfold approach [7, 19] is a powerful tool for studying hydrodynamic (i.e. Gregory-Laflamme) and elastic instabilities of higher-dimensional black holes in the ultraspinning regime and away from it. 1 In this context, one first finds a stationary solution, modelled as a fluid confined to a surface, corresponding to the black hole solution whose stability one wishes to study. The fundamental fluid variables and the geometric properties of the surface describing the equilibrium configuration of the fluid are subsequently perturbed and the stability properties of black holes are found by studying the propagation of hydrodynamic and elastic modes.Black rings can be classified as thin 0 ≤ ν < 1/2 or as fat 1/2 ≤ ν < 1 where for very thin rings ν = r 0 /R is a measure of the ring thickness. Studying Penrose inequalities, the fat branch of black rings in D = 5 has been shown to be unstable [20][21][22] while for the thin branch in D = 5, the instability of black rings relies on numerical studies [6,12]. However, these numerical studies, due to lack of accuracy, have only established the existence of instabilities for ν ≥ 0.144 [6] and for ν ≥ 0.15 [12]. The region ν < 0.144 is left unknown, with the only suggestive arguments of [7,8] being applicable in the strict case of ν = 0, for which there is barely any distinction between the black ring and the boosted black string. Additionally, the numerical studies of [6,12] have not consid...

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Section: Introductionmentioning

confidence: 74%

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confidence: 99%

Instabilities of thin black rings: closing the gap

Armas

Parisini

2019

J. High Energ. Phys.

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“…Since the horizon cross-section must be of positive Yamabe type [18,20], it follows that low temperature horizons in spacetime dimension 5 can only have the topology of a spherical space, or S 1 × S 2 . Furthermore, the blackfolds technique [4,5,6] has been used to infer the existence of new horizons, including new black rings, in asymptotically anti-de Sitter and asymptotically flat spacetimes. The approach also suggests black rings in de Sitter spacetime, but not in the low temperature limit (for bounded horizon area).…”

Section: Introductionmentioning

confidence: 99%

A Bakry-Émery Almost Splitting Result With Applications to the Topology of Black Holes

Galloway,

Khuri,

Woolgar

2020

Preprint

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The almost splitting theorem of Cheeger-Colding is established in the setting of almost nonnegative generalized m-Bakry-Émery Ricci curvature, in which m is positive and the associated vector field is not necessarily required to be the gradient of a function. In this context it is shown that with a diameter upper bound and volume lower bound the fundamental group of such manifolds is almost abelian. Furthermore, extensions of well-known results concerning Ricci curvature lower bounds are given for generalized m-Bakry-Émery Ricci curvature. These include: the first Betti number bound of Gromov and Gallot, Anderson's finiteness of fundamental group isomorphism types, volume comparison, the Abresch-Gromoll inequality, and a Cheng-Yau gradient estimate. Finally, this analysis is applied to stationary vacuum black holes in higher dimensions to find that low temperature horizons must have limited topology, similar to the restrictions exhibited by (extreme) horizons of zero temperature.

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