[Physics] Why must a singularity form inside a black hole?

black-holesevent-horizongeneral-relativitymattersingularities

What is the exact reason that normal matter can not exist within an event horizon?

I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less than its Schwarzschild radius and an event horizon forms around it.

But why can't the neutron star remain inside the event horizon as it was before the event horizon formed? Aside from the escape velocity at the surface reaching $c$, what actually changed?

Why must all matter within an event horizon undergo complete physical collapse to a point?

Best Answer

Basically, the reason is that if the matter is to keep a positive mass, the amount of force required to keep the matter distribution stable tends to infinity once the matter is fit within the schwarzschild radius for that given mass. This was proven in a very strong sense, without much in terms of assumptions about the particular form of the metric, by Roger Penrose and Stephen Hawking in the '60s:

http://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems

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