Undergrad Dissolving Event Horizon w/Charged & Rotating BH

[arusse02]

I saw a fascinating video from PBS space time about dissolving an event horizon. See here for reference:



The video addresses rotating kerr black holes and charged black holes, but doesn't talk about the combination of rotation and charge. So what happens when you spin up the black hole as much as possible so that its an extremel black hole, and then on top of that you start adding electrons with such a trajectory that it still contributes angular momentum? Does the outward pressure of the black hole rotation and the charge combine, thus letting us easily produce a naked singularity? Or is there some effect such that adding electrons to a rotating kerr black hole would somehow expand the event horizon just enough to prevent a naked singularity? Thanks.

 

[PeterDonis]

I saw a fascinating video from PBS space time

This is a pop science video and is not a good source for learning the actual physics.

The video addresses rotating kerr black holes and charged black holes, but doesn't talk about the combination of rotation and charge.

Combining rotation and charge doesn't add anything qualitatively new.

is there some effect such that adding electrons to a rotating kerr black hole would somehow expand the event horizon just enough to prevent a naked singularity?

Yes. When you work out the details, it turns out that however you try to add angular momentum or charge to a near-extremal hole, you have to add enough mass along with it to keep the hole from becoming super-extremal (which is what would be required to form a naked singularity).

 

[Ibix]

So what happens when you spin up the black hole as much as possible so that its an extremel black hole, and then on top of that you start adding electrons with such a trajectory that it still contributes angular momentum?

The electrons have mass, and need kinetic energy if they are going to contribute angular momentum. That mass and energy contribute to the mass of the hole at least as much as is necessary to keep it from becoming super-extremal. And as you add electrons and the black hole becomes charged you have to give the electrons more energy to get them to the event horizon, since like charges repel.