# Is the spin of a black hole affected by the matter orbiting it?

It's well understood that the moon has an effect on how much the earth spins. My understanding is that if the moon was bigger, it could impact tidal forces to a larger extent, and possibly slow the rotation of the earth.

An article by space.com titled "This Huge Black Hole Is Spinning at Half the Speed of Light" describes that black holes could be rotating at 50% the speed of light.

Can we tell if the speed of a black hole's rotation is impacted by the amount of matter orbiting it?

• Only side remark: The moon is slowing earth's rotation by tidal forces and somewhen in the future the earth will stop spinning. The earth did the same to the moon already, which is smaller. The moon shows us always the same face, because rotation around its axis is today synchronuous with rotation around the earth. Aug 13, 2021 at 6:22
• @CharlesTucker3 As you point out: the Moon's rotation is tidally locked to the angular velocity of the Earth-Moon system; the spin of the Moon is one rotation per month (I'm not sure whether that version of 'month' has a name of it's own. Should maybe be called 'tidal lock month'). Given enough time the Earth's rotation will also become locked to the angular velocity of the Earth-Moon system. That angular velocity will be slower than the current angular velocity of the Earth-Moon system, but not zero Aug 13, 2021 at 6:54
• @Cleonis Cleonis, That is true! By the way, you have a very nice homepage ;-)! Aug 13, 2021 at 8:34

Is the spin of a black hole affected by the matter orbiting it?

Spin (angular momentum) of a black hole could be changed by interaction with the surrounding matter in a variety of ways.

• The laws of black hole thermodynamics would be respected in such processes. This, in particular, means that the area of the event horizon will always be increasing even when rotational energy is being extracted from the black hole. Also, angular momentum of black hole would satisfy $$J (where $$M$$ is the black hole mass), it is impossible to spin up the black hole beyond this bound.

• If a body plunges into a black hole its angular momentum (mostly angular momentum of its orbital motion but also any intrinsic angular momentum it had) becomes part of the black hole's. So if a black hole is surrounded by accretion disk, then transport of angular momentum within and into the black hole is an important aspect of processes happening there and this transport would occur via a lot of means: plasma turbulence, magnetic fields, electromagnetic and gravitational radiation etc. Over the course of its evolution accretion could “spin up” black hole quite close to maximum possible values of angular momentum (for a given mass).

• It is possible to transfer angular momentum (and energy) to a black hole via tidal effects see e.g. this paper. For example, this would happen if a black hole is part of a binary (with another black hole, neutron star etc.). This is the direct generalization of Earth's rotation slowing by the tidal influence of the Moon as mentioned in the OP. When placed in identical environments, a rotating black hole absorbs more energy and angular momentum from tidal effects than a nonrotating black hole. But even for rotating black holes under most circumstances this type of mass/angular momentum absorption is too small and could be usually ignored.

• Rotating black holes exhibit superradiance, a phenomenon when the flux of radiation (electromagnetic or gravitational) impinging on a black hole is amplified. This effect is conceptually similar to Penrose process only for waves rather than particles. The necessary energy and angular momentum carried away is supplied by black hole's rotation, and it slows down as a result. A related concept is the black hole bomb, a runaway superradiant process.

• Finally, special mention should go to Blandford–Znajek process which extracts rotational energy (and thus slows down the black hole's rotation) via magnetic fields from external sources.

• Great answer +1: “accretion could ‘spin up’ black hole quite close to maximum” - Could you please clarify what it means when people say, “a black hole rotates at a half the speed of light”? The coordinate speed of light at the horizon is zero, so what exactly moves with “a half the speed of light”, relative to what, and what value does this “speed of light” have? Aug 14, 2021 at 17:01
• Presumably this refers to equatorial radius of event horizon multiplied by angular velocity $\Omega_H$ of event horizon (see e.g. Visser's review of Kerr BH). For extreme ($a=M$) black holes we would then get precisely the speed of light, for smaller spins this “speed” would be smaller. Anyway, I agree, the phrasing is imprecise. Note, that original paper does not have such phrasing (they just estimate “spin parameter”) but MIT news article has. Aug 14, 2021 at 20:15

Let me first recapitulate:
The tidal interaction in the Earth-Moon system is raising the altitude of the Moon orbit, and slowing down the Earth. There is also exchange of angular momentum. The angular momentum of the Moon is increased in the process, and there is a corresponding decrease of angular momentum of the Earth.

In the case of a black hole: The only interaction with surrounding matter, as far as I'm aware of, is with the accretion disk of the black hole.

At large distance to the black hole the gravity from the black hole is very precisely described with the standard newtonian inverse square law of gravity. At distances like that orbital motion around the black hole is as stable as the orbits of the planets of the Solar system.

Closer to the black hole relativistic effects become significant. Long term orbital motion is still possible, but those orbits have precession (Like Mercury has precession of its orbit) The closer to the black hole, the faster that rate of precession.

So anything orbiting a black hole at that range has an increased probability of bumping into neighbours. The effect of such a bump is loss of orbital altitude. (Or the bump makes the orbit even less circular, which increases probability of bumping into neighbours.)

It's not that the black hole is actively pulling mass towards itself. It's more that over time mass that is orbiting a black hole tends to lose orbital altitude. Eventually the mass that is orbiting the black hole loses so much orbital altitude that it crosses the event horizon.

When orbiting mass crosses the event horizon the orbital angular momentum is absorbed into the overall angular momentum of the black hole.

(Many black holes have clean surroundings. All mass that was close enough to be gobbled up has already been gobbled up.)

What that means is that a black hole has only one form of gravitational interaction with surrounding matter: orbital altitude of surrounding matter decreases, and eventually that matter crosses the event horizon. (By contrast, the tidal interaction in the Earth-Moon system causes increase of Moon orbit altitude)

So in the normal course of events I don't see a process that could decrease the angular momentum of the black hole.

(Well, I suppose the following scenario is possible: a moving gas cloud meets a black hole, and the angular momentum vector of that gas cloud is in the opposite direction to the angular momentum of that black hole. If that gas cloud contracts to an accretion disk then you have an accretion disk with an angular momentum that is opposite to the angular momentum of the black hole. But that is a very contrived scenario.)

So:
I don't see a plausible process that could make the angular momentum of a black hole come back down again.

For fun you can read up on the Penrose process

No, because almost all matter close to a black hole is so small that their gravity isn't that much.