Black holes die hard: Can one spin up a black hole past extremality?

Abstract

A possible process to destroy a black hole consists on throwing point particles with sufficiently large angular momentum into the black hole. In the case of Kerr black holes, it was shown by Wald that particles with dangerously large angular momentum are simply not captured by the hole, and thus the event horizon is not destroyed. Here we reconsider this gedanken experiment for a variety of black hole geometries, from black holes in higher dimensions to black rings. We show that this particular way of destroying a black hole does not succeed and that Cosmic Censorship is preserved.

Cosmic censorship and parametrized spinning black-hole geometries

“…Instead, it turns out that cosmic censorship is still preserved, for most of the geometries considered, with few very special exceptions. Together with previous results on Kerr [5] or charged BHs [31,32], higher-dimensional BHs [6] and BHs in non-asymptotically flat spacetimes [10,30,33,34], our results indicate that destroying event horizons is a difficult task. We remain as ignorant as before on the precise reasons for this.…”

“…For higher values of rotation a (naked) singularity becomes visible to asymptotic observers. It turns out that it is impossible -at least in a perturbative regime -to spin-up the spacetime beyond the extremal a = M value with pointlike particles 1 [5,6,7,8,9,10], in accordance with the spirit of the Cosmic Censorship Conjecture (CCC) [11]. Even in fully nonlinear and extremely violent processes, such as the collision of two equal-mass Kerr BHs, the CCC seems to be preserved [12,13,14].…”

Overcharging higher-dimensional black holes with point particles

“…Like all previous work [11,16,17,35], we assume that the particle energy E fully accretes to the ADM mass of the black hole. The ADM mass upon absorption of the particle then simply increases as M → M + E while the ADM charge increases as Q to Q + q.…”

Thermodynamics with pressure and volume under charged particle absorption

“…conducted on the conjecture for not only black holes of Einstein's theory of gravity, but also anti-de Sitter (AdS), lower-dimensional, and higher-dimensional black holes [18][19][20][21][22][23][24][25][26][27][28][29][30]. From a thermodynamic point of view, the conjecture is quite consistently related to the laws of thermodynamics.…”

“…Specifically, the denominator of dS h has a negative value for the extremal black hole. So, 19) which means that the entropy of the black hole decreases at least for the extremal case for all dimensions, D ≥ 4. Therefore, the second law of thermodynamics is violated under the consideration of the P V b term for the charged particle absorption.…”