What happens when black holes collide? Does one black hole “consume” the other? Do they become a larger black hole? Does it get more dense or just larger?
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I don't know how to address the "consume" question. If you were pulling on a piece of fabric and two tears in it grew until they met each other to become one tear... would you say that the larger one consumed the smaller?
Wait, really? So if you had a super massive disk that was just 1 electron away from having enough mass to become a black hole... and then an electron popped into existence due to quantum randomness... then it would become a sphere instantly? Wouldn't that violate the speed of light or something?
Your disk will emit a lot of gravitational on electromagnetic radiation, and after a while it will be a nice sphere. (Unless it's rotating and it will be a nice somewhat-elipsoidal ball.)
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> and then an electron popped into existence due to quantum randomness
I feel there is a huge can of worms of technical problems in this sentence that nobody know how to solve for now. Just in case replace the quantum randomness with a moron with a broken CRT used as an electron cannon.
Event horizons are non-physical. Better to think of it as "then a spherical event horizon would become apparent." When the mass within a given black-hole-shaped volume (spherical for non-rotating mass) is "one electron short" of being a black hole, then one can define a surface in the shape of the (future) black hole where the escape velocity is /just/ below the speed of light. In practice, all light emitted within that volume will already be captured by the mass, unless it's perfectly perpendicular to the (future) event horizon. When that extra electron is added, it becomes true that the escape velocity at that same surface is now the speed of light -- the definition of event horizon. But nothing needs to "form" to make this true.
> a sphere instantly
The concept of instantly doesn't work with time dilation like this. What you see will be different depending on if you are also falling in, or if you are far away.
Perhaps if it were exceptionally wide the whole disc wouldn't collapse. Maybe only the parts near it's center. In that case you'd end up with a large ring around a neutron star. Add a bit more mass and maybe it's now a ring around a black hole. The gravity of the ring might distort the event horizon in some way, I'm not sure quite how, but probably its possible to get a non-spherical hole in situations where the objects distorting the shape are still in the universe.
But as for the matter lost into the hole, it's gone. If the hole were to retain some shape based on what's "inside" of it, that would be the kind of information leak that the laws of physics do not permit.
The event horizon is the imaginary line across the river which once passed, even if you paddle as quickly as you can, you won't be able to get away from the waterfall. Once you pass that line, you're bound to reach the waterfall eventually.
Now, thanks to Maxwell and Einstein, we know there's a maximum speed that anyone can paddle, the speed of light, and so we define the event horizon to be relative to this speed.
You can calculate the event horizon for just about anything. The main difference between a black hole and everything else, is that for a black hole the event horizon is larger than the object itself.
For example, the event horizon of a neutron star with a mass of 1.4 solar masses and a radius of 10km is about 4.1 km, well inside the neutron star. Thus you don't get the "black hole effect", since once you pass the surface of the neutron star the matter above you pulls you away from the center.
The river analogy is actually not far off what they try to use as an analog for testing black hole predictions, effectively a large water tank with a drain hole. Sixty Symbols did a video on this way back[1], and this thesis[2] goes into the details. Some are going beyond water using liquid helium to simulate quantum black holes this way[3].
[1]: https://www.youtube.com/watch?v=kOnoYQchHFw
I'm not sure if we can measure the shape of black holes, but I'm sure everyone think they are spheres with a slight deformation due to rotation.