How fast can a black hole rotate?

Abstract

Kerr black holes have their angular momentum, $J$, bounded by their mass, $M$: $Jc⩽G{M}^2$. There are, however, known black hole solutions violating this Kerr bound. We propose a very simple universal bound on the rotation, rather than on the angular momentum, of four-dimensional, stationary and axisymmetric, asymptotically flat black holes, given in terms of an appropriately defined horizon linear velocity, $v_H$. The $v_H$ bound is simply that $v_H$ cannot exceed the velocity of light. We verify the $v_H$ bound for known black hole solutions, including some that violate the Kerr bound, and conjecture that only extremal Kerr black holes saturate the $v_H$ bound.

10 pages, 2 figures, Essay written for the Gravity Research Foundation 2015 Awards for Essays on Gravitation and selected for Honorable Mention

References in corpus (3)

• Scalarized Hairy Black Holes
• Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
• Proof of the angular momentum-mass inequality for axisymmetric black holes

Cited by in corpus (40)

• Kerr black holes with Proca hair
• Spinning black holes in Einstein--Gauss-Bonnet--dilaton theory: non-perturbative solutions
• Kerr black holes with self-interacting scalar hair: hairier but not heavier
• Astrophysical imaging of Kerr black holes with scalar hair
• Effective stability against superradiance of Kerr black holes with synchronised hair
• The superradiant instability regime of the spinning Kerr black hole
• Excited Kerr black holes with scalar hair
• Spinning black holes in shift-symmetric Horndeski theory
• No-scalar-hair theorem for spherically symmetric reflecting stars
• Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell
• Black holes with synchronised Proca hair: linear clouds and fundamental non-linear solutions
• Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime
• The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field
• Kerr black holes with synchronised scalar hair and higher azimuthal harmonic index
• Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field
• Charged reflecting stars supporting charged massive scalar field configurations
• Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell
• No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
• A bound on energy extraction (and hairiness) from superradiance
• No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
• Kerr black holes with synchronised axionic hair
• Onset of superradiant instabilities in rotating spacetimes of exotic compact objects
• No hair for spherically symmetric neutral black holes: nonminimally coupled massive scalar fields
• Magnetized accretion disks around Kerr black holes with scalar hair - I. Constant angular momentum disks
• Stationary bound-state scalar configurations supported by rapidly-spinning exotic compact objects
• Violations of the Kerr and Reissner-Nordstrom bounds: horizon versus asymptotic quantities
• Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordström black-hole spacetime
• No hair for spherically symmetric neutral reflecting stars: nonminimally coupled massive scalar fields
• Ultra-spinning exotic compact objects supporting static massless scalar field configurations
• Magnetized accretion disks around Kerr black holes with scalar hair -- Nonconstant angular momentum disks
• Spinning boson stars and hairy black holes with non-minimal coupling
• The Reissner-Nordström black hole with the fastest relaxation rate
• Horizon geometry for Kerr black holes with synchronised hair
• No-go theorem for static boson stars
• The spinning Kerr-black-hole-mirror bomb: A lower bound on the radius of the reflecting mirror
• Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars
• No-short scalar hair theorem for spinning acoustic black holes in a photon-fluid model
• Stationary scalar clouds supported by rapidly-rotating acoustic black holes in a photon-fluid model
• No-go theorem for spatially regular boson stars made of static nonminimally coupled massive scalar fields
• How short can stationary charged scalar hair be?