This one has been bugging me, so I'm hoping someone can help me through it (I also think it would make a good question to answer on Astronomy Cast).

How does a black hole rotate? I can visualize how objects like planets and stars rotate because they have a finite spherical shape and whole thing is in rotation about the center of mass. But a black hole is a singularity. It's entirety is the center of mass. I understand a little about frame dragging and how a rotating object drags spacetime with it, but again I can't wrap my head around how a singularity could achieve this. I can't even understand it from a conservation of momentum perspective, such as a rotating star collapsing into a black hole, because the distances of any mass in the star to the center of mass goes to zero when the black hole is formed.

If anyone could help me understand, I'd appreciate it.

Thanks,
Steve
Shrewsbury, MA

My question would first be "Is the mass rotating, or is the effect rotating?"

Other than that, I have no other insight.

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I think this is where your understanding departs from science's current, best understanding. There are many discussions on these boards regarding the fact that a singularity is a mathematical "expression" only, and in fact cannot exist in reality.

If you really want insight into black holes, check out Kip Thorne's excellent book, Black Holes and Time Warps, Einstein's Outrageous Legacy [1994]

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Everyone is entitled to his own opinion, but not his own facts.

If photons are the carrier of the electromagnetic force and light cannot escape the event horizon, how can a black hole have charge? Add that to your list of black holes don't make sense questions.

Obviously, our model of a black hole has room for improvement.

As I see it, nothing special happens at the event horizon of a super massive black hole except light that escapes is curved back so that it re-enters the event horizon(local observer). Most of the stuff that falls toward a black hole misses the event horizon and does a slingshot maneuver. This becomes part of the accreation disk which rotates rapidly, and chaotically both inside and outside the event horizon. I don't see how rotation, and spiraling in can be avoided. Is there a physical singularity which rotates? We may never know. My guess is there is a small, very hot and very dense core at the center of the black hole, with the matter being converted to energy by the extreme conditions, including rapid rotation. A micro black hole (if there are any) is the same except the event horizon is below the surface of the very dense, very hot core, which is smaller than a proton. Neil

I disagree that the singularity is necesarily hot.

Not hot? Is that because heat is defined as molecular movement and no molecules can exist near the singularity? Perhaps it is because the singularity has zero meters radius? How can nothing have a temperature? If the black hole absorbed only one one watt second in the last billion years, the watt second can't escape, so is it not, at least warm near the singularity?
I would expect stuff near the sigularity as it takes time to stuff, stuff into a zero meter radius? Even photons? Neil

For whatever reason, the mathematics of BHs as currently understood tell us that mass, charge, and momentum are the only measurable qualities outside the event horizon. They may have qualities that we can't currently measure, or that are "hidden" behind the horizon, or something else entirely; looks like a satisfactory answer will have to wait for quantum gravity.

In any event, I second the recommendation of Kip Thorne's text.

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As Cougar suggests, this is where you get hung up. The singularity is only part of the complex affair that we call a black hole. The singularity is just a point, or small collection of points, deep inside the black hole where our mathematical theory of physics fails, and we no longer have the ability to physically interpret the mathematics. But the black hole is in fact an extended region of spacetime surrounding the singularity. When we look at a black hole from far away the singularity is hidden from our view by the event horizon. If you are going to say "a black hole is ..." something, it makes more sense to say it is an event horizon rather than a singularity, because the event horizon is something we can physically interact with. So now that we understand the extended nature of the black hole, we can more easily grasp the idea of rotation.

The size of the black hole is not too hard to get at. Just look up "Schwarzschild radius" and you can get the mass dependent radius of a non rotating Schwarzschild black hole, which is good enough for this discussion (rotating black holes are more complicated, but not significantly different in size). So a black hole with the same mass as Earth would only be about 8.8 millimeters in radius, not very impressive on the cosmic scale of things. Even a black hole as massive as the sun has a radius of only about 2.9 kilometers. Not much for size, but with the same mass, and therefore the same gravity, as our sun, it would gravitationally dominate the space around it just as our sun gravitationally dominates the solar system. The black hole at the center of our galaxy is about 3.7 million times the mass of the sun. For that we get a schwarzschild radius of about 10,000,000 kilometers, or about 0.07 astronomical units. That may still seem small, but anything that massive is gravitationally hard to ignore (see, i.e., the UCLA Galactic Center Group webpage)

Now that we have all that figured out, the last thing to remember is that a black hole is not a solid object with a solid surface, the way we usually think of it. White dwarfs, neutron stars, even exotic quark stars and such are all still solid objects with solid surfaces. It's easy to understand rotation of a solid object. But in the case of a black hole, it is not a solid object that is doing the rotating, it is the region of space time that is the black hole that is doing the rotating. Whatever it was that became a black hole, maybe a star, or a whole lot of stars, must have had some angular momentum associated with it. That momentum must still be conserved, it can't just vanish. So the spacetime that is the black hole inherits the angular momentum of the progenitor, and the black hole rotates.

Finally, I will point out that solid surfaces & event horizons are observationally distinguishable, one from the other. Material that falls on a solid surface behaves differently from material that falls on an event horizon. This difference can be used to observationally infer the presence of an event horizon around a compact object, and therefore observationally distinguish between solid objects and black holes in candidate objects. This has been done, and it is fair to say that we have observationally segregated black holes from non black holes in a few cases (i.e., Remillard, et al., 2006; Done & Gierlinski, 2003; Paul, et al., 1998).

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What makes you think the singularity even has a property called temperature? Temperature is the average kinetic energy of a group of particles. Try to picture a singularity jiggling around with a temp of millions of degrees.

I do not expect particles within the singularity to have kinetic energy. In fact, I do not expect known particles to be present at the singularity.

Does not escape and dive back in. It never escapes.

Also keep in mind that we infer the existence of black holes. The non-rotating Schwarzchild solution to the GR equations is a special case.

Does that mean that mass can not only be converted into energy, but also into spacetime?

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I'm not sure that's a valid question. The angular momentum simply won't go away. The mass is constant, just highly condensed. Neither is converted into 'spacetime', it's just that all we think we will observe is a tiny bit of rotating spacetime. (It might be a good idea at this point to define what you mean by spacetime.)

Again, remember, we don't have a laboratory-size black hole to study. It is difficult to think that the objects at the centers of galaxies, and the supernova remnants, and whatever it is that is generated by the super-energetic cosmic rays hitting our atmosphere, and maybe CERN particles, are not black holes; and if they are,the last two cases are going to generate a lot of useful information. Maybe we will even get a clue as to what the quantum properties of black holes are. It's a shame the name black holes stuck; gravitationally collapsed objects is a lot better description.

Well, mass can be converted into energy, and therefore into motion, which can put you into a different inertial reference frame, which affects the passage of relative time; I don't know if that's the same as "converting into spacetime", but it does have an effect on spacetime.

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