How fast can a black hole rotate?

TL;DR

This paper proposes a universal bound on black hole rotation based on horizon linear velocity, which is constrained by the speed of light, and verifies it across various solutions.

Contribution

It introduces a new universal bound on black hole rotation using horizon linear velocity, applicable even to solutions violating the Kerr bound.

Findings

The horizon linear velocity cannot exceed the speed of light.

Known black hole solutions satisfy the proposed velocity bound.

Extremal Kerr black holes are conjectured to saturate the bound.

Abstract

Kerr black holes have their angular momentum, $J$, bounded by their mass, $M$: $Jc\leqslant GM^2$. 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.