How fast can a black hole rotate?

Abstract

Kerr black holes (BHs) have their angular momentum, J, bounded by their mass, M: Jc <= GM(2). There are, however, known BH 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 BHs, 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 BH solutions, including some that violate the Kerr bound, and conjecture that only extremal Kerr BHs saturate the v(H) bound.