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

TL;DR

This paper investigates whether self-force effects can prevent a Kerr black hole from being overspun beyond its extremal limit when a particle is thrown in, using perturbation theory and deriving conditions for cosmic censorship.

Contribution

It provides a comprehensive analysis of self-force effects on overspinning scenarios, extending previous work by including the full self-force impact and deriving a necessary and sufficient censorship condition.

Findings

Overspinning occurs only with particles from infinity.

Self-force effects can prevent overspinning through dissipative and conservative mechanisms.

A new inequality condition determines when overspinning is overruled.

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.