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It is known that - When a star collapses during the formation of the black hole, the black hole obtains the spin of the star which it collapsed from...

What I'd like to know is, If this spin accelerates as a result of angular momentum (if any), What effects could this rapid rotation have on the black hole, its gravity or anything else around it?

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This is question is both open theoretically and experimentally, although there is some astrophysical data.

After a black hole forms, the matter is squeezed as it falls into an accretion disk, and the matter that is absorbed is rotating very fast by the time it falls in. The dynamics of the accretion disk are complicated, because there are horrendous fields caused by ionization and charge separation. This makes it difficult to achieve consensus about whether the matter falling into a small black hole causes its spin to slow down or speeds up.

The experimental consensus seems to currently be that the black holes that power active galactic nuclei are spinning at close to extremality, meaning they have close to the maximum amount of angular momentum for their mass. One reason to expect this is that, absent quantum mechanics, the black hole can only generate energy to the extent that it is spinning. The AGN's are generating a huge amount of energy, so something must be maintaining the spin, and this should be the infalling matter.

It is my opinion that there is still uncertainty regarding the emission of highly spinning black holes, because there is no certainty about what happens to infalling matter. One has reasons to suspect that this matter is emitted from the black hole nonthermally, more or less as it came in, after doing a traversal of the interior regions. If this is so, you must take into account the spin-up/spin-down effects of the in-out matter, and this requires the classical limit of quantum black hole, something which is nearly, but not quite, available, thanks to string theory.

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I have never heard a single person talk about quantum gravitational effects being important for AGN. SMBH should be very, very, nearly classical at the horizon. – Jerry Schirmer Sep 3 '12 at 3:37
@JerrySchirmer: You haven't heard it because I am the only one who says it, so stackexchange has the scoop. The quantum gravity is for coming out of a black hole. You can't calculate coming out classically. It doesn't come out semiclassically in this universe, but there is no other universe for it to come out in, so if it comes out, it must be in this universe. This process cannot be comprehended classically. Most people will tell you it doesn't come out quantum mechanically either, but bollocks, I say. – Ron Maimon Sep 3 '12 at 5:49
you don't know that. It's highly speculative, and not tied to any calculation I know of, or that you've provided. Extreme conclusions require extreme evidence. This answer is not science. – Jerry Schirmer Sep 4 '12 at 3:48
Unpublished results that contradict what the entire astrophysics community thinks about realistic, physical black holes with no observational evidence? That's going to require more for me than vague heuristics on stack exchange. Also, the two horizons converge for extremal BH. – Jerry Schirmer Sep 4 '12 at 15:24
@JerrySchirmer: I am wary of using Arxiv, as I don't have Arxiv permission and it is not open to anyone anymore. The first thing Cornell did when they got Arxiv is to shut down access by requiring an authority endorsement, and this stranglehold on submissions can be exploited for censoring people. I don't trust these people, they already forbid cold fusion papers. This stackexchange expressly encourages original research, that's the whole point. As far as "technical level", I don't know what that means--- I explained the method, the reason, but not the gluing. Maybe I'll go Vixra. – Ron Maimon Sep 6 '12 at 16:03

The black hole gains the angular momentum of the matter that falls into it, minus the anglar momentum of the outgoing gravitational radiation. There are a lot of questions currently on the site regarding the effects of a spinning black hole. The primary one is that the black hole will cause the space around it to co-rotate with the hole.

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