(Now with part 2.)
General relativity is known to be a approximation. Which is good, because black holes are an extremely screwed up idea, which I'll now show without a single iota of math.
Physicists are very worried about information being destroyed by black holes. I find this very funny, because time dilation won't actually allow an outside observer to ever see anything cross an event horizon; the dilation grows without bound as an object approaches the horizon, and it would take an infinite amount of time to see it cross, which is the physicist way of saying it will never happen. A black hole would be very cluttered with falling objects, and would appear so except that the time dilation makes things disappear; the rate of interaction falls with the speed of all processes of the falling object, so eventually it takes an excruciatingly long time to emit even a single black-body photon. (This photon is also red-shifted into oblivion.)
To make this outside observation consistent with the inside observation, the universe appears to speed up dramatically. While the position, velocity, and acceleration of a falling observer move the apparent event horizon, I strongly suspect the rest of the black hole will evaporate through Hawking radiation long before the observer actually sees itself reach the point where the horizon should be. (Although an observer would never survive; between the Hawking radiation it is in the way of, the tidal forces, and the infalling radiation of the rest of the massively sped up universe, any order in the falling object will be utterly annihilated. You'd have to construct something that was forged into an observer by these forces, which doesn't seem possible, and even if you did it would also have to forge some incredible shielding to survive more than an instant.)
There's a problem, of course. The event horizon is exactly at the Schwarzchild radius. When an object above the Chandresekhar limit starts to collapse, at time zero it has an event horizon radius of zero. Actually, there are an infinite number of zero-size event horizons, everywhere, the same way even static objects would be just waves with frequency zero. Anyway, the zero-size black hole at the centre of the Chandresekhar object would start to grow. As soon as it grows to nonzero size,* there will be an event horizon...which stops anything from falling in within finite time. A black hole event horizon should contradict its own formation, which actually makes sense, since the black hole is supposed to form when one of the equations describing nature goes singular.
*(can't use Planck metres, as this is a General Relativity object; we don't know how to make Planck units consistent with GR, or even if we need to or not.)
It gets worse, though. Assume the event horizon doesn't actually prevent its own formation, somehow. As the matter in the Chandresekhar object collects at the event horizon, it will fall beneath its own Schwarzchild radius, presumably allowing the event horizon to grow outward.* In addition to time dilation, gravity produces length contraction, and event horizons provide an infinite amount of both. As the event horizon moves outward, it will inevitably, according to outside observers, compress the infalling matter to zero size.
*(It really hurts to try to consider this seriously. It falls in, but can't ever reach its own Schwarzchild radius because of the event horizon just slightly beyond that, which means that event horizon will feel the same things, which means it won't actually reach its own Schwarzchild radius, which means...argh...)
So, err, where is the mass coming from, again? Admittedly this will coincide with the matter reaching the event horizon; crossing the event horizon and reaching zero size (and zero temporal speed) are the same event.
And, it gets even worse. Black holes evaporate through Hawking radiation. As the event horizon contracts, these zero-size objects need to reappear. According to itself, it has never crossed the event horizon. So, furthermore, they need to reappear in the right place.
Think about that for a second. How does the black hole know where to reconstruct these zero-size objects? The information should be lost, (Zero! Size! Objects!) which means that as soon as it contracts at all, it should start reconstructing them either all at once in random positions, or just at random in general, which would mean that the infalling observer either can't see anything consistent with outside observers, or else falling into a black whole results in random teleportation. Or, you know, the objects that contribute to black hole masses don't exist anymore, so they don't need to reappear, but which means black holes...don't actually have mass?
So apparently I shouldn't be laughing at the worries about physical information loss after all.
From this, it makes sense to assume that the black holes we see - dark gravitation lenses - are dark simply because of time dilation, which stabilizes them from ever falling beyond their Schwarzchild radius; lacking an event horizon it can't actually go infinite, but as the density rises it can become very high. As a result, no event horizon forms and Hawking radiation may or may not actually exist. Right now, the derivation assumes an event horizon and finds that it splits virtual particle pairs, preventing them from annihilating, nonlocally stealing energy from the black hole. Without an event horizon, something similar may occur, perhaps due to quantum tunneling of time-dilated matter or something similar, or simply tidal forces causing the particle pairs to separate and then one half annihilating real time-dilated matter instead of its virtual pair.
Which illustrates the nonlocality; this annihilation event releases gamma photons and the like, which are usually absorbed by the vacuum. How does the gamma photon know it was released in a virtual interaction instead of a real one, so it knows to disappear? Either the energy debt is itself nonlocal, which would mean any random gamma photon can pay it back, or the gamma photon has to somehow know which direction to be emitted in, so it can go fill the nonlocal hole at the point of virtual particle instantiation. Honestly this just makes me think either negative energy is real, meaning virtual particles are not pairs but at least triads, which would have incredible technological applications, or else virtual particles are also an approximation.
The Schwarzchild radius was not calculated by actually following the chain of events, which is why you don't normally read about this stuff. Schwarzchild simply calculated the gravitational field of a general nonrotating sphere, and found a term that can go singular. Simply setting the radius to less than this value essentially assumes the mass formed out of whole cloth inside the event horizon. Similarly, trajectories inside the black hole are calculated after assuming the event horizon already exists. In general, solving dynamic GR equations is basically impossible, so I would not be surprised, nor hold it against them, if nobody has ever actually successfully simulated a stellar collapse.
The degeneracy pressures are also calculated in general, rather than dynamically, which is fine for "What would happen if?" but you'll only find something is impossible if there is an internal contradiction, such as supposing entropy decreases. It's quite possible that rather more complicated logic can show that neutron stars can't form either, although its also very possible that they can.
If black hole event horizons could really swallow things, the universe would not exist. The singularity of the Big Bang was definitely behind its own Schwarzchild radius. Things inside the event horizon can only move toward the singularity and will reach it in finite time. We, that is, all the energy of the universe, would have struck the singularity a long time ago. On the other hand, perhaps all the antimatter is stuck in an enormous gravitational time-dilation lock.
Similarly, if electrons and other fundamental particles were actually point particles, they would be behind their own Schwarzchild radii and instead of atoms we'd just have a very large black hole. The amount of an electron's charge and mass that is inside a zero-size volume is zero, which is why QCD gets nonsense when it assumes it isn't.