End Point of the Ultraspinning Instability and Violation of Cosmic Censorship

Abstract

We determine the end point of the axisymmetric ultraspinning instability of asymptotically flat Myers-Perry black holes in D = 6 spacetime dimensions. In the non-linear regime, this instability gives rise to a sequence of concentric rings connected by segments of black membrane on the rotation plane. The latter become thinner over time, resulting in the formation of a naked singularity in finite asymptotic time and hence a violation of the weak cosmic censorship conjecture in asymptotically flat higher-dimensional spaces.Introduction.-The recent detection of gravitational waves from black hole binary mergers [1,2] has provided the first direct observation of these objects. The current observational data are compatible with the predictions of general relativity, and they suggest that the end point of such mergers is a Kerr black hole (BH) [3]. These observations provide evidence that the Kerr BH in vacuum is non-linearly stable, at least within a certain range of the angular momentum. However, a mathematically rigorous understanding of the stability of the generic Kerr BH, as well as a thorough understanding of its dynamics under arbitrary perturbations, is still lacking. In fact, recent work suggests that novel and nontrivial dynamics may be present very close to extremality (e.g., [4][5][6]).Higher dimensional BHs, however, can be unstable under gravitational perturbations. This was first shown by Gregory and Laflamme (GL) for black strings and black p-branes [7]. Determining the end point of this instability has been a subject of intense study due to the potential implications on the weak cosmic censorship conjecture (WCC) in such spacetimes. With the aid of numerical relativity (NR), [8] found that the GL instability gives rise to a self-similar structure of bulges connected by ever thinner string segments, which all undergo the GL instability. Eventually, the black string pinches off in finite asymptotic time, resulting in a naked singularity. Since no fine-tuning of the initial data was required, this result constituted a violation of the WCC, albeit in spacetimes with compact extra dimensions.Contrary to the D = 4 case, asymptotically flat BHs in higher dimensions can carry arbitrarily large angular momenta. At very large angular momenta, BHs become highly deformed and resemble black branes, which are known to be unstable under the GL instability [9]. This observation highlighted the possibility that higher dimensional asymptotically flat BHs can be unstable under gravitational perturbations. This indeed turned out to be the case. For instance, the black rings of [10] suffer from various types of instabilities [11][12][13][14][15][16], including the GL instability. The non-linear evolution of the latter was studied in a very recent work by three of us [15], where it was found that, for sufficiently thin rings, the evolution of the instability is similar to that of the GL instability of black strings. Hence, a naked singularity should form in finite asymptotic time, thus violating the WCC in higher-dimensio...

Mass–Angular-Momentum Inequality For Black Ring Spacetimes

“…This result is particularly striking because recent numerical work, focusing on dynamical black rings [19] and 'ultraspinning' black holes [31], suggests violations of WCC occur in D ≥ 5. Although our proof is given for bi-axisymmetric initial data, the same result is expected to hold for small perturbations away from biaxisymmetry, which is the regime where the numerical studies are set.…”

Weak cosmic censorship conjecture for a Kerr-Taub-NUT black hole with a test scalar field and particle

“…A general proof of the conjecture is still beyond reach and it is one of the most outstanding unresolved problems in classical gravity theory [2]. It is known that there are some methods to test the conjecture, such as numerically analyzing gravitational collapse of a scalar field or other matters [3][4][5][6][7][8], numerical simulations of collision and merger of two black holes [9][10][11], analytically and numerically evolving perturbed black rings or black holes [12][13][14][15][16][17]. One way we are interested in is to ask whether it is possible to destroy a black hole horizon.…”

Black ripples, flowers and dumbbells at large D

“…In this paper, we explore the phase space of compact stationary solutions with a single spin in the large D limit, specifically, we focus on the (non-)axisymmetric deformed families branching off from the Myers-Perry family. The instability of ultra-spinning MP black holes and the existence of nearby 'rippled' solution was first conjectured in [34] and later, after the proof of existence of the zero modes and the instability [35][36][37][38][39], the rippled solutions were constructed numerically and identified as solutions that connect to black rings and black Saturns [4,[40][41][42].…”