On the formation of black holes

[Ring]

IIRC with a Kerr black hole the radius of the event horizon actually decreases as it’s angualr momentum increases,

I think it depends. If the increase in angular momentum is due to incoming matter, then the matter can’t avoid bringing in more energy than angular momentum, and therefore the horizon expands.

A question: If a spinning black hole is extremal, then any incoming matter that would create a naked singularity will miss the hole. Why?

[Chronos]

A question: If a spinning black hole is extremal, then any incoming matter that would create a naked singularity will miss the hole. Why?

It won’t necessarily miss the hole, but if it does get in, it’ll have to be forced in. Whatever is doing the forcing will add enough extra energy into the system that the mass will still increase faster than the specific angular momentum, so it’ll stay decently-clad.

[Alka_Seltzer]

@Ring

Relativistic mass is a bad concept for this very reason; it causes too much of this type of confusion.

As I said above, reading between the lines I think that is what confused the OP’s friend.

[Ring]

@Chronos

It won’t necessarily miss the hole, but if it does get in, it’ll have to be forced in. Whatever is doing the forcing will add enough extra energy into the system that the mass will still increase faster than the specific angular momentum, so it’ll stay decently-clad.

I guess I should rephrase my question: If a spinning black hole is extremal, then, in the absence of an external force, any incoming matter that would create a naked singularity is guaranteed to miss the hole. Why is that?

My guess would be that frame dragging causes the matter’s geodesic to curve around the hole?

[Lumpy]

@Whack-a-Mole

A question that occurred to me while reading this (hope it is not too much a hijack):

If I get in my never-runs-out-of-fuel-but-no-bigger-than-a-car-impossible-rocket and accelerate continually my mass increases right?

Will I eventually collapse into a black hole or is there something about my reference frame (the scale in my rocket accelerating at a constant 1g claims I still weigh 70 kilos) that means no black hole?

@Ring

Good heavens no Whack-a-Mole. We’ve been over this a thousand times on this board. Relativistic mass is a bad concept for this very reason; it causes too much of this type of confusion. Let’s say someone else is going as fast as you. Will he think you’ve gained mass?

Of course not. Mass is equal to the energy of a system that cannot be transformed away.

I don’t know about unchanging velocity (Special Relativity), but couldn’t you collapse into a black hole if you accellerated quickly enough(General Relativity)?

[Ring]

@Ring

I guess I should rephrase my question: If a spinning black hole is extremal, then, in the absence of an external force, any incoming matter that would create a naked singularity is guaranteed to miss the hole. Why is that?

My guess would be that frame dragging causes the matter’s geodesic to curve around the hole?

After some Googling, Wald says that due to the high impact parameter the particle will miss the hole. I guess I can see this. The lower the impact parameter the lower the ratio of imparted angular momentum to energy and “a” would stay less than “M.”

So to increase this ratio, and get “a” to be greater than “M” you’d have to have a high impact parameter, and thus it would miss the hole.

[Chronos]

That’s one way it happens, of course, but you could also try to take an object spinning on the same axis as the hole, and drop it in along that axis. I think what happens there is that you get a repulsive gravitomagnetic force that keeps it out, but I’d have to double-check.

[Ring]

@Chronos

That’s one way it happens, of course, but you could also try to take an object spinning on the same axis as the hole, and drop it in along that axis. I think what happens there is that you get a repulsive gravitomagnetic force that keeps it out, but I’d have to double-check.

Yep, that’s exactly what happens. I stumbled on it while I was searching for the other stuff. The author used it to explain why a particle with intrinsic spin also couldn’t drive “a” greater than M.

[sisu]

Sounds a lot like the things we used to talk about as teens, oh and boobs.

Absolute space. The time between the last suck on the bong and passing out!