Rotating Black Holes | Angular Momentum Explained

[DBrant]

Hello, all.

Here's something that just came to mind... (and forgive me if my reasoning is naive)

When a star collapses to become a neutron star, its angular momentum is conserved, so neutron stars can rotate very quickly. Now, if it collapses further to a singularity, won't its angular momentum approach infinity (no matter how slowly it was spinning before)? How can there be a black hole with a finite angular momentum?

By that same logic, wouldn't any infinitely-rotating black hole automatically become a naked singularity?

 

[smallphi]

If angular momentum is conserved it won't approach infinity but remain the same. You are mixing angular momentum with angular speed. The angular speed of rotating black hole is defined at the horizon not at the central singular point, so it won't approach infinity either.

 

[pervect]

Hello, all.

Here's something that just came to mind... (and forgive me if my reasoning is naive)

When a star collapses to become a neutron star, its angular momentum is conserved, so neutron stars can rotate very quickly. Now, if it collapses further to a singularity, won't its angular momentum approach infinity (no matter how slowly it was spinning before)? How can there be a black hole with a finite angular momentum?

In your analogy, the angular momentum doesn't become infinite - you even said it was conserved! meaning it's constan! - but the rotational speed becomes infinite.

GR is a bit different. The space-time of a rotating black hole in the exterior region would be described by the Kerr metric. It isn't really possible to assign the angular momentum an exact location, but it is in some sense "spread out" by the gravitational field, rather than being concentrated at a point.

The general issue with momentum (and energy) here is that there isn't any simple way of assigning it a location. So we can say that it's "spread out", but we can't describe exactly where. Rather, we can describe exactly where it is in many different ways, none of which can lay claim to being special. But all of these different ways agree on the total amount.

Note also that the interior structure (inside the event horizon) of a rotating black hole is still a topic under research. The Kerr metric works fine for the exterior region, but is felt to be unstable in the interior region. I could dig up some references to papers by Penrose and Israel if there was some interest, but they are rather technical.