Feynstein100 said:
Doesn't the spacetime curvature of a region depend on the density of matter-energy in that region?
No. For example, spacetime near Earth is a vacuum, but is curved due to the Earth nearby.
Feynstein100 said:
As far as I know, the only way to get infinite curvature is to have infinite mass-energy density,
Actually, black hole solutions like the Schwarzschild black hole are vacuum everywhere.
Feynstein100 said:
I don't see how you can have one without the other.
That's the problem with not using the maths.
Feynstein100 said:
All black holes have some angular momentum, thus making them Kerr black holes
Kerr black holes also have singularities, albeit with a more complex structure. They are also "moments in time", again with some caveats.
Feynstein100 said:
Would rotation solve the problem of world lines terminating?
No.
Feynstein100 said:
Although, that in itself raises an interesting question. That while Schwarzschild black holes don't exist in nature, it is possible to artificially convert a Kerr black holes into a Schwarzschild one by stealing its angular momentum. What would happen in that case? Hmm
It is in principle possible to spin-down a black hole. However, a black hole that you do this to is neither Kerr nor Schwarzschild, since those solutions both have fixed angular momentum. And the problem of singularities existing within is an extremely general one - they're inevitable in an extremely broad class of spacetimes that includes any kind of black hole that doesn't contain exotic matter.
Feynstein100 said:
However, I believe that, at least for physics anyway, even though the mathematical details might be complicated, the underlying principle/logic itself should be able to be expressed in plain English. If you can't do that, then it kind of implies that you don't really understand it.
No, it implies that a language developed by apes to tell each other where the tasty fruit is and coordinate stabbing mammoths isn't great at describing the interiors of black holes. Scientists don't use maths for fun. It's the only language we have to talk about these things well enough to understand them.
Feynstein100 said:
Yes, I am aware of this but what does this mean physically?
You understand what a moment in time is, surely. The whole universe at exactly 6am tomorrow, for example. You can't avoid it because it's the future.
The singularity isn't exactly like 3am tomorrow, because the curvature invariants aren't infinite at 3am tomorrow, but it has the important characteristics: you can't avoid it and there's only so much you can do to delay it.
Feynstein100 said:
why is this not a problem for the electron?
If we had a theory of quantum gravity we could tell you, but we don't so we can't. General relativity assumes its sources of gravity are classical continuous matter, and attempts to create a theory that can handle quantum sources are ongoing. A theory of quantum gravity would also hopefully provide a correct explanation for what goes on inside black holes where GR says there are singularities.