Overspinning a Kerr black hole: the effect of self-force

Abstract

We study the scenario in which a massive particle is thrown into a rapidly rotating Kerr black hole in an attempt to spin it up beyond its extremal limit, challenging weak cosmic censorship. We work in black-hole perturbation theory, and focus on non-spinning, uncharged particles sent in on equatorial orbits. We first identify the complete parameter-space region in which overspinning occurs when back-reaction effects from the particle's self-gravity are ignored. We find, in particular, that overspinning can be achieved only with particles sent in from infinity. Gravitational self-force effects may prevent overspinning by radiating away a sufficient amount of the particle's angular momentum ("dissipative effect"), and/or by increasing the effective centrifugal repulsion, so that particles with suitable parameters never get captured ("conservative effect"). We analyze the full effect of the self-force, thereby completing previous studies by Jacobson and Sotiriou (who neglected the self-force) and by Barausse, Cardoso and Khanna (who considered the dissipative effect on a subset of orbits). Our main result is an inequality, involving certain self-force quantities, which describes a necessary and sufficient condition for the overspinning scenario to be overruled. This "censorship" condition is formulated on a certain one-parameter family of geodesics in an extremal Kerr geometry. We find that the censorship condition is insensitive to the dissipative effect (within the first-order self-force approximation used here), except for a subset of perfectly fine-tuned orbits, for which a separate censorship condition is derived. We do not obtain here the self-force input needed to evaluate either of our two conditions, but discuss the prospects for producing the necessary data using state-of-the-art numerical codes.

25 pages, 4 figures

References in corpus (6)

• Test bodies and naked singularities: is the self-force the cosmic censor?
• Destroying a near-extremal Kerr-Newman black hole
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Transition from adiabatic inspiral to plunge into a spinning black hole
• Gravitational self-force in nonvacuum spacetimes
• Combined gravitational and electromagnetic self-force on charged particles in electrovac spacetimes

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• Weak Cosmic Censorship Conjecture in Kerr-Newman-(Anti-)de Sitter Black Hole with Charged Scalar Field
• Thermodynamics and Weak Cosmic Censorship Conjecture in Nonlinear Electrodynamics Black Holes via Charged Particle Absorption
• Massless charged particles: Cosmic censorship, and Third law of Black Hole Mechanics
• First law of black hole thermodynamics and the weak cosmic censorship conjecture for Kerr-Newman Taub-NUT black holes
• Extending the weak cosmic censorship conjecture to the charged Buchdahl star by employing the gedanken experiments
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• Overcharging a multi black hole system and cosmic censorship
• The topological RN-AdS black holes cannot be overcharged by the new version of gedanken experiment
• Test fields and naked singularities: is the second law the cosmic censor?
• Distinguishing Signature of Kerr-MOG Black Hole and Superspinar via Lense-Thirring Precession
• Stability of horizon with pressure and volume of d-dimensional charged AdS black holes with cloud of strings and quintessence
• Overspinning problem in Kerr black holes: second order corrections and self-energy
• Challenging the cosmic censorship in Einstein-Maxwell-scalar theory with numerically simulated gedankenexperiments