Infinite density is pretty crazy though. Would it change much from the outside perspective if there was something more like an ultra compact neutron star at the center?
There can't be anything like that at the center; that kind of solution doesn't work. At least, not if there is an actual event horizon.
The most likely solution, IMO, is that there is no actual event horizon, and the horizons we are seeing in our observations are only apparent horizons. There are theoretical possibilities such as the "Bardeen black hole" (which is misnamed since it has no actual event horizon) that look like standard classical GR black holes from the outside for a time on the order of the Hawking evaporation time, which means we would not be able to observe the difference now or for the foreseeable future. But what is deep inside those solutions is not any kind of ordinary compact object like a neutron star.
Because no ordinary object, i.e., object made of ordinary matter obeying an ordinary matter equation of state, can be that compact. It's not possible.
Solutions like the "Bardeen black hole" adopt a different equation of state in their deep interior, something more like dark energy, which is not any kind of "ordinary object". That is the only way to have an object that compact without an event horizon. The missing piece in such solutions is how that kind of equation of state could arise as a result of something like stellar collapse: that is where some kind of new physics, possibly some form of quantum gravity, might be needed.
If so, then a followup: why can’t we imagine an object of arbitrary density sufficient that the massive object is also small enough? Why does it need to be a mathematical discontinuity or otherwise goofy universal exception-to-the-rule? We obviously can’t observe it, so isn’t it simply that the mathematics expresses the fact that we cannot observe it?
No, it isn't. It is impossible for a stable compact object made of ordinary matter that is smaller than the event horizon size for its mass to exist. In fact it is impossible for a stable compact object made of ordinary matter that is smaller than 9/8 of its event horizon size to exist. This result is known as Buchdahl's Theorem.
The one thing I'm not 100% sure on is whether an event horizon can form. I have never been able to shake the feeling that with Hawking radiation giving each black hole a large but finite lifetime and with matter falling in beyond the infinite future (to outside observers) you'd have the incoming matter encounter the death of the black hole before it can fall in. This would make a black hole a kind of explosion powered by Hawking radiation that looks frozen in time to outside observers.
Lacking a complete theory that can adequately explain both Hawking radiation and general relativity it's quite hard to know if this makes any sense. Though I can't rule out an answer already exists but is simply not known to me.
No. Your wrong claim about the slowing of time flow has nothing to do with those.
> Have you read the Kerr paper?
Yes. It doesn't say anything like what you were saying. I have commented on it elsewhere in this discussion.
Any GR textbook. I referenced two classic ones elsewhere in this discussion.
Or, for that matter, you could read the classic paper by Oppenheimer and Snyder which was the first published model of actual gravitational collapse to form a black hole. And was published in...1939. What I'm saying is not news.
> Time stopping at the event horizon is quite the standard view in "science communication" of black holes.
That's because "science communication" sucks at accurately portraying the actual science.
Completely agree.