A few misconceptions/open questions that have appeared in this thread need to be cleared up:
Jason R Carrico said:
if a neutron star is just on the cusp of having enough mass to be a black hole, and then gains that mass, what's to say it doesn't just gain an event horizon at that point?
This is not possible; there is not a continuous series of stable (i.e., non-collapsing) states between any neutron star and any black hole. The reason is something called Buchdahl's Theorem, which says that no stable configuration of matter can have a radius smaller than 2.25M, where 2M would be the Schwarzschild radius of a black hole with the same mass. So there's no way for a stable object like a neutron star to be "just short" of being a black hole, because that would correspond to a stable configuration of matter having a radius of, say, 2.0001M--i.e., just a bit larger than a black hole of the same mass--and that is ruled out by Buchdahl's Theorem.
rootone said:
an infalling something reaches the (theoretical) singularity very shortly after crossing the event horizon.
Why?, because the infalling thing is trying to go faster than light
This is not correct. No locally measured speed will be faster than light, even inside the horizon. A coordinate speed in particular coordinates might be greater than ##c##, but this has no physical meaning. And none of this has anything to do with whether a singularity is present or how long it takes an infalling observer to reach it.
Jason R Carrico said:
Why wouldn't everything approaching the event horizon already be traveling at or near the speed of light?
It is, relative to an observer "hovering" at a constant altitude just above the horizon. Only local relative speeds are physically meaningful in a curved spacetime.
Jason R Carrico said:
how do we know it's not a super compact body?
Because no compact body can exist with a radius smaller than 2.25M. See above.
stefan r said:
I thought there was a time uncertainty too. I may have misunderstood the Eintein-Bohr debate.
The Einstein-Bohr debate is irrelevant, as is the uncertainty principle; we are talking about classical GR here, not QM. If you want to talk about how quantum gravity might affect possible black hole states, please start a new thread (and it should be either in the QM forum or, more likely, the Beyond the Standard Model forum, since there is no established theory of quantum gravity at present).
Ken G said:
General relativity is normally thought to imply that anything that creates an event horizon around itself will also collapse into a singularity. I personally don't know what theorems are needed for that conclusion
The Hawking-Penrose singularity theorems are the ones that establish this conclusion: a good brief statement of the conclusion is that the presence of a trapped surface implies geodesic incompleteness. The assumptions required are an energy condition (which one depends on what kind of geodesic incompleteness is being addressed--timelike or null) and a condition on the global structure of the spacetime (typically that there is a Cauchy surface with certain properties). The Wikipedia page gives a decent brief overview:
https://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems