# Limit of angular momentum and "alone" black hole singularity

I just read in a book that a black hole has an angular limit at which the event horizon would disappear, leaving the singularity alone. This question is not about this said statement — even though I do question it; how can a singularity be alone? (the exact wording is the following, although translated: "… the event horizon would shatter leaving naked the central singularity.") — but about this limit: the speed of light.

If a black hole has a rotational momentum higher than the speed of light it breaks apart, but since it is impossible to go faster than the speed of light, wouldn't that simply be impossible? That would only be possible if the angular momentum maximum was higher than the speed of light, hence this confusion.

The frame dragging (rotation of space) is already the speed of light at the ergosphere and even faster inside of it, so that is not a limit that prevents a higher spin.

What prevents higher spins for black holes is that the centrifugal force becomes larger than the centripetal force at that small radii, therefore a star with higher spin can not collapse to a black hole. The frame dragging of a maximally rotating black hole will also deflect prograde particles that want to enter, so you can't increase its spin by feeding it that way either.

But even if there was a way to pop the outer event horizon of a physical black hole you probably would not get a naked singularity but the former star shrunk to about the size of the inner Cauchy horizon or a nonsingular torus, since the ring singularity of the Kerr vacuum solution is gravitationally repulsive and therefore unlikely to form from collapsing matter, at least according to Roy Kerr himself.

If what you're referring to is the Kerr black hole's angular momentum limit, the issue with angular momenta beyond the limit is not necessarily that the black hole would fall apart - the black hole is a one-dimensional ring singularity in this case - but that spacetime would be bent in such a way that the event horizon's radius is zero or imaginary.

Rotating objects, including black holes, sort of "drag" spacetime along with their rotation. This is a well-confirmed effect called frame dragging, related to gravitomagnetism, which is a consequence of the geometries of spacetime that correspond to rotating objects. In the extreme case of a Kerr black hole which has passed its angular momentum limit, the frame dragging effect becomes so strong that it allows for an observer to get arbitrarily close to the singularity without crossing an event horizon - hence, no event horizon exists.

This is problematic of course, so it is conjectured that black holes have a hard angular momentum limit to prevent naked singularities.

• Thank you for answering, although I still have some confusion. Is the angular momentum limit inclusively the speed of light and only a black hole rotating at 100% of c would tear apart? Commented Sep 4 at 21:58
• The issue isn't that $c$ is the rotation speed limit for the black hole's stability - the singularity is universally stable - but if it rotates beyond a certain speed, the event horizon disappears and the singularity becomes naked. Commented Sep 4 at 22:25
• That clears things up ^^ thanks Commented Sep 4 at 22:36