Towards a 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., [4-6]). 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 space-times. 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 mo-menta. 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 asymptot-ically 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 [11-16], 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-dimensional asymptoti...

Attempts at vacuum counterexamples to cosmic censorship in AdS

“…The endpoint of this instability is not known although there has been some remarkable recent numerical progress [6]. It may in fact violate weak cosmic censorship in vacuum [7,8]. In our case, the ergoregion is in the asymptotic region and it is not clear if a superradiant instability exists, since ingoing waves are partially absorbed by the horizon and return with smaller amplitude.…”

Charged black hole bombs in a Minkowski cavity

“…In the latter case, the mass of the bosonic field effectively provides a potential barrier that traps the bosonic waves near the horizon. From the superradiant studies in rotating AdS black holes it is conjectured that superradiant instabilities should evolve following one of two possible scenarios [12,[15][16][17][18][19][20].…”

Collapse and Nonlinear Instability of AdS Space with Angular Momentum

“…This region is therefore a natural place to study the rotational superradiant instability [65,[76][77][78][79][80][81][82] for which little is known fully dynamically. However, typical growth rates for this instability are around 10 −5 [68], which requires a longer simulation than we can feasibly perform with our methods.…”

“…Furthermore, our ansatz implies that such a study will necessarily be incomplete. High angular wavenumbers are expected to play an important role in this instability [65,[80][81][82], but our ansatz is restricted to only the m = 1 azimuthal wavenumbers. …”