All rotating black holes will eventually stop?

[espen180]

According to Wikipedia:
Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.

By this logic, won't all rotating black holes eventually stop spinning? Or are there processes by which a black hole can gain angular momentum? If so, what are these?

 

[bcrowell]

According to Wikipedia:
Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.

By this logic, won't all rotating black holes eventually stop spinning? Or are there processes by which a black hole can gain angular momentum? If so, what are these?

In the example of a stellar-mass black hole that has an accretion disk of material that it's eating from its companion star, conservation of angular momentum says that any material that vanishes out of the companion must give its angular momentum to the black hole. I would expect the typical black hole to either have constant angular momentum (if it has no companion and no accretion disk) or increasing angular momentum (if it has an accretion disk).

I could be wrong, but I believe the Penrose mechanism is somewhat more speculative. I think it's one of the mechanisms that's been proposed to explain relativistic jets. Relativistic jets come out in a narrow beam along the rotation axis, so I wouldn't expect them to carry away much angular momentum...?

 

[Chronos]

A black hole is a bit complicated. What is it that you think is rotating? The accretion disk is defintely rotating, but, not the singularity. What do you think would have a braking effect on the singularity? The singularity sheds mass via Hawking radiation, but, is otherwise oblivious to the universe.

 

[bcrowell]

A black hole is a bit complicated. What is it that you think is rotating? The accretion disk is defintely rotating, but, not the singularity. What do you think would have a braking effect on the singularity? The singularity sheds mass via Hawking radiation, but, is otherwise oblivious to the universe.

This is incorrect.

The black hole itself can have angular momentum, not just the accretion disk: http://en.wikipedia.org/wiki/Kerr_black_hole

The singularity can exchange angular momentum with the rest of the universe. If it couldn't, then its angular momentum would be undetectable.

 

[espen180]

So a black hole eating a companion star will have a continuously increasing angular mometum?

 

[Frame Dragger]

As bcrowell said, yes it DOES have angular momentum down to the singularity. It's that very problem that lead to Einstein and Rosen postulating the (mathematical) existence of a ring singularity and their "bridges".

Secondly, the black hole is not "oblivious to the universe". One way or the other it interacts with the universe (maybe behind an event horizon, maybe not). It emits thermal radiation and can lose, and by "feeding" gain mass. Infalling matter carries its own angular momentum, but in the absolute absene of infalling matter and continuing Hawking Radiation... a black hole that is rotating will not stop doing so as a result of evaporative thermal process. What happenes to black holes when they fully radiate... IF they do... is a subject of conjeture. Probably they go "boom".

Imagine the future thusly... the universe continues to expand (which it may), and all matter is eventually consumed by black holes, stars, pulverized in impacts, ablated by radiatin and decay... etc. You would expect black holes to have a similar endpoint if they obey thermodynamic laws; they should eventually release all of their mass as thermal energy, leading to a net increase of the entropy of the closed system that is our universe. Neat, eh?

 

[Frame Dragger]

So a black hole eating a companion star will have a continuously increasing angular mometum?

Pretty much every answer here is encapsulated in the following post from the archives of this site.

There are several different radii by which the hole can be defined. The one that is most often thought of is the Event Horizon, so named because that is the distance from the centre beyond which no event can be witnessed. The reason for that is that the escape speed exceeds c at that point, so light that would reveal the event can't get out to be seen.
Hawking radiation comes from the Ergosphere.Actually, Hawking Radiation (HR) "comes from" the edge of the Event Horizon (EH) which is the classical 2GM/c2. This EH is at the same radius for a rotating BH as it is in the classical (non-rotating) BH. But, all BH's rotate and that is where the Ergosphere comes in. Roy Kerr showed that a rotating BH also has a "second" EH, the ergosphere, in the shape of an oblate spheroid with the ergosphere and the EH meeting at the poles of the axis of rotation. Anywhere off the poles and the EH is "inside" the buldge of the ergosphere, so you can visualize the BH as having two EH's. A particle, and photons, between the EH and the ergosphere can escape the BH since the "inside" EH is actually where the radius = the escape velocity of c.

Forgeting the ergosphere for the moment, an old post of mine (on HR and EM production)was:This (vacuum fluctuation) energy will produce virtual-particle (VP) pairs and not just electrons as has been mentioned so far. The VP pair is produced by "borrowed" energy from the BH. The Heisenberg uncertainty principle allows for two things here. (1) It allows the VP pair to exist on borrowed energy for a finite, but very short, period of time, and (2) it allows the VP pair to be of any energy amount as long as, again, anything borrowed is returned. Therefore, the VP pair is not limited to just electrons and positrons being discussed so far, it can also be quarks, protons, neutrons, and certain mesons regardless of energy required to produce the pair.

So, one of the "virtual" particles falls back into the BH and the other becomes a "real" particle with real mass. If it escapes into space (sometimes both will fall back in), then the mass of whatever the escaping particle was will exactly match the mass-loss of the BH. Mass is delivered into the realm of real and the BH loses that much mass, so the first two laws of thermodynamics are still happy, nothing has been violated.

How does a small BH become so hot and evaporate so fast? Well, the "standard" HR process just mentioned was about one, single VP pair. In a large BH idling along this might be the case here and there around the EH. But, in a smaller BH with more energy per squareanymeasure will be producing VP pairs, of many different particle types, at a great pace. Now we have a swarm of real particles buzzing all around the EH at a very high density. Some will combine into more complex particles, but most will just escape or, to produce the intense energies mentioned, many particle-antiparticle pairs will meet and annihilate into pure energy. If the density is high enough and the particles massive enough, you will see the gamma-ray production Chronos mentioned, again, especially from small, short-lived BH's. Of course, it is actually the entire EM spectrum of photons, and many particles, that are produced but the gamma rays get the most attention.so, in a rotating BH, particles are produced between the classical EH and the ergosphere, and that is where an object (any mass + photons) CAN escape back into the space away from the BH.
In Hawking radiation, pair production of particles from pure energy occurs at the ergosphere. One particle falls in, but the other makes a run for it and takes some of the hole's energy with it. In that manner, the hole can 'evaporate'.True except that it is not the ergosphere as explained above.

As far as the ergosphere in concerned, it is this space (area) between the EH and the ergosphere where an object approaching the BH can gain energy and exit with more energy than it had on approach. This is as long as it does not also enter the EH and be lost forever. This effect, not Hawhing Radiation, can also cause the BH to lose mass, but, the energy added to an escaping particle in this case is provided by the angular momentum of the BH. And, since the BH loses angular momentum, it loses energy. Once again, a loss of energy = a loss of mass since mass = energy.

Gets confusing, don't it..

That