Title says it all I think.
Why is a spinning black hole different than one that doesn’t? How do we even know one from another? Why is it important to make that distinction? How does a singularity spin?
If I was falling in to a black hole would a spinning one be any different to me than one that is not spinning?
A static (non-rotating, neutrally charged) black hole, e.g. the Schwarzschild metric, is the most general spherically symmetric of the Einstein field equations. Because of that symmetry, it is ‘easy’ to calculate the trajectory and effects upon a body entering the ergosphere of a black hole because it is coincident with the event horizon, so you can’t get any kind of closed timeline curve fuckery or any kind of frame dragging (Lense-Thirring) effects that would be experienced with a rotating black hole. These effects are described in brief in the linked article:
The effects of frame dragging on nearby objects can be significant, especially for objects in close proximity to a massive rotating body. One of the most well-known consequences of frame dragging is the Lense-Thirring precession, which refers to the gradual rotation of the orbit of a test particle around a rotating mass.
In addition to precession, frame dragging can also lead to the twisting and warping of spacetime in the vicinity of a rotating object. This can have implications for the stability of orbits, the behavior of accretion disks, and the overall dynamics of the system.
Any real naturally-occurring black hole will have angular momentum because any not-perfectly-symmetric collection of mass coalescing into a singularity will inevitably develop some tangent component of momentum about the collective center of mass, so all black holes are at least Kerr metrics (non-charged rotating axisymmetric black hole). In addition, while you don’t ask about charge, it is likely to the point of certainty that all naturally-occurring black holes have some small degree of net charge so the most simple real world black hole is described by the Kerr–Newman metric (charged rotating axisymmetric black hole).
As far as your experience of falling into a black hole (assuming it is massive enough that the gravitational gradients won’t tear you into component atoms), there are subtle differences due to frame dragging that you might be able to observe between a rotating and non-rotating black hole but unless you are on a trajectory going straight toward the singularity you wouldn’t casually observe them. You would just observe the gravitational lensing effects shown in the video below (although it doesn’t seem to have the red shift corrections that an in-falling observer would witness):
Below is a Wired magazine “Explains in Five Levels of Difficulty” video featuring astrophysicist and science communicator Dr. Janna Levin of Columbia University. You can jump to whatever level you are comfortable with but I think you’ll want to start with the “College Student” at 8:50:
Stranger
Why is spinning even important for a Black Hole? How does an Event Horizon spin?
I get that everything will spin because of conservation of angular momentum. I’m just not sure why this matters with a Black Hole.
The event horizon can be a torus and the singularity can be a ring.
I don’t know how to answer the question of “Why is spinning even important for a Black Hole?” except to say that at a large scale every system some kind of angular momentum. There is no intentionality, purpose, or intrinsic meaning in the existence of a black hole. The rotation is just a consequence of aggregating a bunch of mass in differential motion, just as your toilet swirls when you flush it even though the water in the bowl doesn’t have any volition about how it moves.
It might help to consider that a black hole isn’t really a material “thing” in conventional physical terms. The singularity itself can essentially be treated as a large composite particle with just the properties of mass, charge, and spin, and it can’t really directly interact with any other system except by absorbing it. The event horizon and the ergosphere (and other mechanical properties) are really effects that occur in the plenum of spacetime around it, so just as a wave in the ocean is just an expression of kinetic energy in water but doesn’t exist as a physical object that can be captured and studied in isolation, the black hole is just a consequence of a highly concentrated amount of mass-energy stretching and warping spacetime.
Stranger
The short answer as to why it’s important is frame dragging. An orbit around the black hole in the same direction as the hole’s angular momentum will be different from one in the opposite direction. In particular, if you go in the correct orbit around a hole, and drop some mass into the hole at closest approach, you can actually leave the hole with more energy than you went in with, the extra energy coming from stealing some of the hole’s rotational energy.
Also very important is the angular momentum of all of the stuff around the black hole, which will usually be in approximately the same direction as that of the hole itself. This will result in all of that stuff forming a fairly thin accretion disk, and shape the beams of energy that result from stuff falling in.
A black hole has a maximum possible amount of spin that’s proportional to its mass. We expect that most black holes in the Universe are pretty close to this maximum spin, about 90% of maximum.
The singularity of a spinning black hole is a ring, but the event horizon can’t ever be a torus. Even for a maximally-spinning black hole, the horizon is still an ellipsoid.
Perhaps intuition would be helped by leaving the black hole out of it to start. A non-spinning planet warps spacetime in a spherically symmetric way. A spinning planet warps spacetime in a twisty way. If you slowly crank up the density of these hypothetical planets, that spinning vs. non-spinning differences remains. You can tell whether the object is spinning or not just from how spacetime is warped. If you keep cranking the density up, eventually the curvature gets extreme enough to lead to additional qualitative features in spacetime (due to the black hole you just created), but the spinning vs. non-spinning differences remain despite those new features.
So, just as a planet might be spinning (i.e., have angular momentum), so too might a black hole.
How does frame dragging happen? Stranger_On_A_Train’s link just compares it to a spinning top on a rubber sheet twisting the sheet itself. What actually happens?
I’d like to know more about that myself. I’ve gone to the Wikipedia page on frame dragging several times over the course of the past decade or so and I can’t make heads or tails of the math. In addition, intuitively, it seems a lot more implausible than a lot of already-weird stuff like quantum mechanics and special relativity.
Any non-handwaving answer to that question would require first teaching general relativity in a non-handwaving way. Which is generally a graduate-level, or at least high undergrad, course.
Besides what others have said, it’s because that’s one of the three characteristics of a black hole that matter.
The no-hair theorem, also known as the black hole uniqueness theorem, states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, angular momentum, and electric charge.[citation needed] Other characteristics (such as geometry and magnetic moment) are uniquely determined by these three parameters, and all other information (for which “hair” is a metaphor) about the matter that formed a black hole or is falling into it “disappears” behind the black-hole event horizon and is therefore permanently inaccessible to external observers after the black hole “settles down” (by emitting gravitational and electromagnetic waves). Physicist John Archibald Wheeler expressed this idea with the phrase “black holes have no hair”, which was the origin of the name.
Black holes are simple, to the point of that being one of the weirder things about them. Their spin is important because that, mass and charge are their defining qualities.
Ok…
How does a singularity spin?
How does an event horizon spin?
How can we measure the spin of a black hole?
It’s measured by how it distorts light.
And it spins by, well, spinning just like any other object.
It is a mathematical abstraction. An abstraction that says, “here be dragons”. Spin makes no sense as the entire point of a “singularity” is that our understanding at this point has ceased. There is no actual object, so nothing to spin.
The event horizon is also just a mathematical abstraction. There is no specific physical manifestation of anything at the event horizon. If you passed it, you would not know. Just that your future becomes rather limited. So there is nothing specific at the event horizon to spin. The location of the event horizon is dependent on the spin.
By measuring the effect of the spin on spacetime outside of the black hole. Which becomes a matter of measuring the frame dragging.
As noted above, shoot a set of objects around the black hole in different directions. Observe their velocity when they come around again. Depending on the black hole spin they will have different velocities. Those that ran around with the frame dragging will get faster. Those that went around opposite get slower. Orthogonal, no effect.
At a greater distance frame dragging could be observed with more sensitive instruments that measure anomalies in direction over time. We have measured frame dragging around the Earth, albeit at the absolute limits of detect ability, but matching theory within those limits.
That is, at least conceptually, exactly how it happens; the angular momentum of the central mass results in a distortion of the adjacent spacetime plenum such that a body traveling near it is ‘pulled along’ with the stretching of spacetime. This means that the angular circumference around the mass is somewhat less than 2𝞹 (or 360°), so it can be observed in that effect as it is with the anomalous precession of Mercury. As @Chronos notes, actually modeling or calculating that effect requires really understanding the Einstein field equations in a rotating coordinate frame, which is graduate-level coursework.
The ‘singularity’ has an effective moment of inertia which is described by its effect on local spacetime; it obtains angular momentum because the mass that it absorbed to create a black hole had net angular momentum, and it often acquires more as it grows in size. The ‘event horizon’ isn’t really a physical object; it is just a boundary in the metric tensor of spacetime at which all ‘world lines’ (the paths that a particle can take) form geodesic curves which cannot recross that boundary; that is to say, the point at which even a photon is forced into a closed orbit, never to escape.
The rotation of a black hole (or any other massive object like the Sun) can be measured by anomalous motion as with the example of Mercury above, and also just by the accretion disk which is found around many large black holes in regions with a lot of dust (as in the supermassive black holes at the center of most galaxies) or stellar residues from a stellar companion such as Cygnus X-1, the first black hole to be discovered. It is expected that all naturally occurring black holes will have some amount of angular momentum.
Stranger
I’m guessing that part of the OP’s discomfort with black holes having angular momentum is that the singularity is supposedly a dimensionless point, so has no component parts that can move relative to one another. (The same is true for an electron, which nevertheless has spin, the quantum mechanical analog of angular momentum.) In everyday life, we see that something is rotating by observing the motion of its component parts, but singularities and electrons have no component parts. Perhaps one of the physics folks can address this issue more directly?
Ignorance fought – thank you!
See the post above yours, but one critical insight is that spinning black holes supposedly have a ring singularity, not a point singularity.
Everything else proceeds from the fact that some black holes affect space and matter around them as if they spin. Since mathematical equations predict that they ought to preserve angular momentum, and they have a ring singularity, the best explanation is simply that they spin because they can, should, and seem to.
Surely then, due to conservation of angular momentum, as the rotating mass collapses toward a singularity, its rate of spin should approach infinity?
I’ll ask this another way:
I am floating in space and there are two black holes in front of me. One to my right and one to my left (for this let’s assume they are not orbiting each other).
Is there any way I can tell if one is spinning and the other is not? Also, does it matter at all? Is there any difference worth noting that one is spinning?