Six-dimensional Myers-Perry rotating black hole cannot be overspun

Abstract

Though under non-linear accretion, all black holes in four and higher dimensions obey the weak Cosmic Censorship Conjecture, however they generally violate it for the linear test particle accretion with the exception of five dimensional rotating black hole with a single rotation. In dimension greater than five, there exists no extremal condition for black hole with single rotation and hence it can never be overspun. However it does exist for two rotations of five dimensional rotating black hole and then black hole could indeed be overspun under linear accretion. In this paper we study the case of six dimensional rotating black hole with two rotations and show that unlike the five dimensional black hole it cannot be overspun under linear accretion. We would conjecture that so should also be the case in all dimensions greater than six. Thus CCC may always be obeyed for rotating black hole in all dimensions greater than five.

How do rotating black holes form in higher dimensions?

“…It may not be able to overspin even at the linear order. This is precisely what happens and has been shown in an explicit calculation in [37]. In all dimensions D ≥ 6, a black hole cannot be overspun in [34].…”

Testing the weak cosmic censorship conjecture for a Reissner–Nordström–de Sitter black hole surrounded by perfect fluid dark matter

“…It is worth noting that the study of overspinning of an extremal black hole in higher dimensions shows that neither an extremal black hole could be overspun nor a non-extremal one could be converted into an extremal one under a linear order perturbation [24]. Further the WCCC has been addressed for black holes in dimensions D ≥ 5 [54,59], and the black hole in dimensions D ≥ 6 can never be overspun and always obeys the CCC in the weak form [60].…”

“…Dark matter has not been so far detected directly, yet astrophysical observations indicate that many giant elliptical and spiral galaxies contain a (sometimes a binary) supermassive black hole in the galactic center embedded in a giant dark matter halo [3,4,[65][66][67][68]. In the literature, several black hole solutions with a dark matter background have been proposed (see for example [69][70][71][72][73][74][75][76][77][78]). The analysis of the accretion process for different spherically symmetric spacetime geometries for a static fluid and the accretion of phantom energy onto a stationary charged black hole has been investigated testing under various conditions (see for example [79,80]).…”

Five-dimensional charged rotating minimally gauged supergravity black hole cannot be over-spun and/or over-charged in non-linear accretion

“…In this case there is yet another subtler case of a black hole with single rotation that cannot be overspun even at linear order, however, like all other cases it could be overspun when both rotations are present [45]. However, the six-dimensional rotating black hole with two rotations cannot be overspun under a linear order perturbation [46]. A charged black hole in higher dimensions could always be overcharged at linear order [47].…”