End point of nonaxisymmetric black hole instabilities in higher dimensions

Abstract

We report on the end state of non-axisymmetric instabilities of singly spinning asymptotically flat Myers Perry black holes. Starting from a singly-spinning black hole in D = 5, 6, 7 dimensions, we introduce perturbations with angular dependence described by m = 2, m = 3 or m = 4 azimuthal mode numbers about the axis of rotation. In D = 5 we find that all singly spinning Myers-Perry black holes are stable, in agreement with the results from perturbation theory. In D = 6 and 7, we find that these black holes are non-linearly stable only for sufficiently low spins. For intermediate spins, although the m = 2 bar mode becomes unstable and leads to large deformations, the black hole settles back down to another member of the Myers-Perry family via gravitational wave emission; surprisingly, we find that all such unstable black holes settle to the same member of the Myers-Perry family. The amount of energy radiated into gravitational waves can be very large, in some cases more than 30% of the initial total mass of the system. For high enough spins, the m = 4 mode becomes the dominant unstable mode, leading to deformed black holes that develop local Gregory-Laflamme instabilities, thus forming a naked singularity in finite time, which is further evidence for the violation of the weak cosmic censorship conjecture in asymptotically flat higher dimensional spacetimes.

Black ripples, flowers and dumbbells at large D

“…This process of a black hole developing long arms that end up pinching off has indeed been observed in [28,46], not only for the spindles but also for higher multipole deformations. We find it likely that these dynamical solutions would correspond to the short branches described above, i.e., those resulting from exciting the zero modes in the direction with increasing Ω.…”

“…As already studied in the previous section the large D effective equations allow for stationary solutions without axisymmetry around the rotation axis, the first (and so far only) analytically known solution is the dipolar black bar [27]. Like the other multipolar solutions, the black bar plays an important role in the decay of the ultra-spinning instability of MP-black holes [28,43,46]. At high enough angular momentum the bar gets very elongated and develops a Gregory-Laflamme type instability.…”

“…Putting this into eqs. (3.42) and (3.43), we obtain 46) in which a also should be expanded according to (3.17). We see that the ratio of angular momentum to mass only differs by O ε 2 from the Myers-Perry branch.…”

Cosmic censorship and the evolution of d -dimensional charged evaporating black holes

“…This is because one has to prescribe boundary conditions on the singularities, which we cannot do without understanding what they are. Nowadays we know that naked singularities can form under various circumstances [1][2][3][4][5][6][7][8]10], notwithstanding the (weak) cosmic censorship conjecture, which states that naked singularities should not form from generic initial conditions [11,12]. The strong cosmic censorship goes a step further, demanding that determinism should hold even inside black holes (in practice it requires the inner horizon of a black hole to be unstable).…”

“…After all, we know from the literature that whether naked singularities can form from various processes does depend on the number of spacetime dimensions. For example, some of the earliest examples of naked singularity formation involves pinching-off of black strings (Gregory-Laflamme instability [5][6][7][8]) which takes place in higher dimensions. More recently, it was discovered that there may be topology-changing transitions for Reissner-Nordström de Sitter black holes and Gauss-Bonnet de Sitter black boles in higher dimensions that hint at violation of the weak cosmic censorship [9].…”