One of the more vexing issues in current science is determining just how fast gravity moves. This is an issue because of the fact that, according to current science, nothing can move faster than light. It is a hard limit on the transfer of information about anything and must be held inviolable in all cases. This, however, is necessarily incorrect even according to current science. This is because gravity must move faster than light for current scientific models of black holes to work.
Let us review a few minor points in order for us to clearly define what we are talking about. First, black holes are created by a great lot of matter being compressed, by gravity, into a into either a zero-dimensional point (known as a singularity), or at least an incredibly compact mass of matter that is so close to a singularity that there is almost no difference for most of our purposes. For the sake of brevity, we shall refer to the thing that is either a singularity or functionally indistinguishable from a singularity as a singularity. I assume that this semantic shortcut will not be a problem for most people.
Second, black holes are so gravitationally strong that even light cannot escape from them. This is because light has both wave and particle properties and it is the particle properties of light that allow it to be bent by the gravitational power of large bodies, such as stars, galaxies and the like. In fact, the light-bending power of our sun's gravity has been observed and documented during eclipses, so it is a known phenomenon. And let us also review that what I refer to as light runs across the entire electromagnetic spectrum, of which visible light is a part. Thus, such things as infrared light, X-rays, microwaves and other such rays are also affected by gravity and, as a result, they cannot escape from black holes either.
Third, the area that is generally referred to as the boundary of the black hole is the border known as the event horizon. This border is the point past which nothing -- including light -- can escape the gravitational power of the black hole. Because of this, there is no way for either physical matter or energy to pass the event horizon. Furthermore, there is no way to communicate from inside a black hole to outside a black hole because of this limitation on the transfer of matter and energy. Thus, for all practical purposes, anything that has crossed the event horizon of a black hole has disappeared from existence.
Fourth, the limitation on the event horizon is essentially created by the escape velocity of the black hole. In order for anything, including light, to escape from inside a black hole's event horizon, it must have an initial velocity that is greater than the speed of light. However, because nothing can move faster than the speed of light, nothing can escape from the black hole.
That is the current thought. However, think about this: how is the gravity escaping from the black hole? After all, objects can be sucked into a black hole, they can orbit around a black hole and they can be affected by a black hole, yet the thing that allows the black hole to perform these actions is the gravity that is being sent from the mass singularity at the center of the black hole. In fact, we can measure the mass and rate of spin of a black hole by its gravitational field and, because of that, we are being provided information from inside the black hole. This is theoretically impossible.
If gravity travelled at the speed of light, it should be sucked back into singularity as soon as it is emitted. And, when a black hole is formed, its gravitational field should have collapsed into itself in the same way that the mass collapsed into itself. Then, all that would be left is a singularity of zero size, a fixed mass, infinite density, and no way for anything or anyone to notice that it is there. It could not react with anything in space because it would not occupy any space whatsoever. This seems to be quite incorrect because black holes don't seem to do this.
The other possibility is that the black hole does not become a singularity, but shrinks down to a nearly zero size. The gravitational field would then collapse to either the size of the pseudo-singularity or, possibly, below the size of the pseudo-singularity. If latter option were the case, it would be pretty cool to watch. That's because the gravitational field is the reason the pseudo-singularity would be allowed to shrink to the size of an atom. Then, once the gravitational field lets go of the neutrons, protons and electrons that are now all occupying the same space, the Pauli Exclusion Principle would take over and the pseudo-singularity would explode at about the speed of light or so as every single particle -- in what used to be a gigantic star -- gets out of the way of every other particle at nearly the same instant. This seems like it might be a neat explanation of what happens inside a supernova, but it does not explain why a black hole would be left behind to provide a gravitational field outside its own mass, as sometimes seems to be the case.
However, this would provide a nifty explanation of how a star could lose enough mass to drop below the Chandrasekhar limit and, as a result, avoid having enough mass to become a singularity: a collapsing star that has enough mass to collapse to a black hole would also have its gravitational field collapse. Then, when the gravitational field collapsed enough, the very gravity that held the singularity together would be gone and the star would expel enough matter to drop below the Chandrasekhar limit. And if it didn't drop enough matter on the first try, it will just collapse and explode again and again until it does drop enough matter.
However, if we accept the idea that gravity moves faster than light, black holes would be able to exert gravity outside their singularities without trouble. So the decision for science is which concept is more important to keep: black holes that can exert gravity on the universe around them, or the speed limit set by general relativity.
Admittedly, this is not the only explanation I can think of for black holes exerting gravity. A couple of other options that come to mind are the following:
But let us take the unpopular view for now and say that gravity does actually travel faster than light. If so, how fast does it travel?
The simplest answer that I can come up with is, "Gravity moves at a speed as close to infinity as the center of a black hole is close to a singularity." This is because, as a particle progresses through a black hole, the particle is essentially travelling through what I would like to call a series of event horizons. Entering the initial event horizon makes it infinitely unlikely for the particle to escape. Moving an infinitesimal distance below the event horizon makes it more than infinitely unlikely for the particle to escape. This is because the particle has entered an area with even stronger gravity than the event horizon and it cannot escape from that even stronger gravity. Then, an infinitesimal distance below that previous infinitesimal distance, the likelihood of escaping the black hole is even more than more than infinitely unlikely. This increase continues down to the singularity.
In this integral method of determining concentric event horizons, every movement toward the singularity makes it more impossible to escape because a particle cannot even move upward to the area where it was before. It is impossible for a particle to get closer to the event horizon or even maintain distance from the singularity because a particle would need to be moving faster than the speed of light to escape the gravitational field below the event horizon. Thus, there is no stable orbit for the particle inside the even horizon; it is only possible for it to move downwards.
As a result of this, every level down toward the singularity is that much faster that gravity would need to travel to escape itself. If the singularity is a finite size, then gravity could have a speed limit that is dictated by the size of the singularity itself. However, if the singularity is infinitely small (i.e. it is zero-dimensional), then gravity would need to be moving infinitely fast to escape from the surface of the infinitely dense singularity. Therefore, it seems to me that the upper limit of gravitational speed is dictated by just how singular the singularity at the center of a black hole is.
Well, it's really not all that singular after all. Or at least it doesn't seem possible that there really is a singularity at the center of a black hole.
The problem here is the fact that there are rotating black holes. These are black holes whose singularities are spinning rather than remaining static. Now then, why is this a problem? There are several reasons and we will go through each of them:
There are several problems with this only if black holes eventually do fall into singularities. The most obvious problem is, of course, the fact that a true singularity could not rotate.
In order for something to rotate, there must be something moving around an axis. Whether this is the edge of a spinning sphere or the earth in orbit around the sun, there is some outer bit that is in motion around a central point. But if an object is zero-dimensional, the object cannot rotate because there is no outer extent to move around the axis. Attempting to make it spin would be impossible because the edges could not be made to move in relation to an unmoving central axis because they would be the unmoving central axis.
Furthermore, let us take the situation where a particle was falling through the black hole toward the singularity. In essence, you could say that the collapse of the star into a black hole would be nothing more than this same case repeated for however many atoms/protons/quarks make up a star and it would be effective. So let's run with it and see what we get:
First the particle would be sucked through the event horizon and into the black hole. It would not actually become part of the singularity but would, rather start spinning around it.
As the particle continues its trek around the singularity, it would continue to gain speed, thanks to the conservation of angular momentum, as it continues to spin around the singularity.
As the radius of the particle's rotation decreases, its speed continues increasing until it approaches the speed of light. At this point, according to relativity equations, it would both shrink and gain mass.
"Hah," you might say, "if the particle somehow achieves the speed of light, it cannot get any faster! Therefore, it will continue in its orbital motion around the singularity, creating a stable rotation for the black hole!"
However, if the particle did that, it could not be going in a normal, elliptical orbit around the singularity. The particle would need to travel faster than light to have a stable, elliptical orbit inside the event horizon and it is impossible for a particle to travel faster than light. This is because every motion on the ellipse that tends toward the singularity is, in essence, the particle falling toward the singularity. But the particle would need to be travelling at greater than the speed of light in order to have enough momentum to not continue falling toward the singularity. This is impossible and it, therefore, will not happen.
Furthermore, if the particle were to reach the speed of light while in a circular orbit around the singularity, it would lose energy because circular orbits require energy to be added in order to remain stable. Thus the particle will lose velocity and the only way for the circularly orbiting particle to gain energy is to fall closer to the singularity and, therefore, it will continue falling toward it. Which means you get an F--. Sit at the back of the class.
Continuing along this line, the particle descending through the black hole would approach the speed of light, causing its mass to increase toward infinity. This means that all the particles in the black hole would be approaching infinite mass as they rotated around the singularity, giving the entire black hole a mass approaching infinity. If a rotating black hole were to have a singularity at the center, it would quickly achieve something like infinite mass and, therefore, infinite gravity. Thus, the event horizon of every rotating black hole would expand out to swallow everything in the universe in a very short amount of time. Of course, the infinitely massed particles would also get the singularity in motion and it would be one very weird, spinning, collapsing mass.
Considering how old the universe is and considering that primordial black holes were probably created at the beginning of the universe, it seems that this is not how things work. Otherwise, the entire universe would have been swallowed up by black holes by now.
However, you might say, "But the rotating particles would inevitably be sucked into the singularity, which you previously said could not rotate, so then it will stabilize at the singularity."
As a matter of fact, no, the particle will not reach the singularity because the singularity is a zero-dimensional object. Even if the particle were to approach the singularity, it would also be shrinking as it neared the speed of light and, as a result, it would also be essentially zero-dimensional.
If the particle is rotating around the singularity, it would only continually get closer to it rather than actually hitting it. It could never hit the edge of it because both the black hole singularity and the particle would continue to approach each other, but they would be in one of those "limit" math problems where they would only touch each other after an infinite amount of time. Thus, a particle that rotated around the black hole would never reach a singularity. F--. Sit on the floor in the back of the class.
So if there was a singularity at the center of a rotating black hole, the black hole itself would rapidly gain mass until the mass became infinite and the black hole swallowed the universe, or the black hole itself stopped rotating. However, because rotating black holes do not have roughly infinite mass, they are clearly not centered on actual singularities. Only a non-rotating black hole could reasonably be expected to have a singularity at the center, but any particle that entered the non-rotating black hole and began any rotation around its singularity would quickly turn it into a rotating black hole.
This means that, because black holes rotate and remain at a stable mass that is increased only by the addition of new mass, there is not a singularity at their centers -- even though I already said that it is close enough to be considered a singularity for most considerations.
Incidentally, this creates a situation where there would be an exclusion principle that works below the level of even the Pauli Exclusion Principle. Which is pretty wild, when you get down to it. But in order to find that new exclusion principle, we would probably need to determine just what level of particle we are dealing with that excludes other particles of its ilk. Which means we would need to determine the size of the (not so singular) singularity at the center of a black hole.
Question: So, just how can we determine how large the singularity is?
Answer: Darned if I know. But there is hope. It seems to me that the solution required is that we would need to determine the rate at which black holes rotate, then figure out the maximum speed of a particle on the very edge of the rotating singularity. This would, of course, be the speed of light. However, a black hole with its outer edge rotating at the speed of light would have infinite mass, so the rate of the black hole's rotation would clearly require the particles at the edge to be travelling at a lower speed than that.
What could be done is to measure the rotational rate of many different black holes (which I assume is possible) and use that information to develop velocity/size graphs. Because we are not sure how dense the black holes are, we cannot absolutely know the velocity of the particles on the edge of the singularity. However, we can measure the mass of a black hole by its gravitational effect on nearby bodies and we can measure the revolution rate of the black hole (again, I assume this is possible). With that information, we could at least build graphs showing just how fast a particle on the edge of the singularity would be moving as it compares to the size of the singularity. And the faster a black hole is rotating, the more the possible range of values could be narrowed down, simply because we would butt up against the limit presented by the speed of light.
Other possible methods for determining the size of black holes could include determining the shape of the singularity at the center -- which, it seems, flattens out due to its rotation. This would affect the gravitational field of the black hole, particularly for black holes that are rotating very quickly, and would therefore show the manner in which their increasingly misnamed singularities are spread out over a larger region.
Then, with at least a rough idea of the size of a black hole's singularity, we could begin to come up with equations that will describe the speed of gravity necessary to escape the nearly singular singularity at the center of the black hole. Which, I believe, was entirely the point in the first place.