A black hole is the collection of events that -for outside observers- don't happen at all, even waiting for an infinite amount of time.
The event horizon of the black hole is a region in space-time that contains the collection of the last events visible from a fallen object world-line.
A black hole doesn't suck stuff in, and it isn't black because not even light can escape it, it's just that the space-time geometry is so curved that there is no simply radially out way
This seems like a really good relativistic explanation and so far I think I grasp the important part of it.
The problem now, is that * virtually every other didactic source ever* states the known definition:
A black hole is an object whose mass is so dense that it collapses on itself, forming an infinite dense spot, whose gravitational pull is so strong nothing can escape it, not even light
Okay, this is the traditional definition I'm used to, but this leaves me wondering: why do we say that not even light can escape it.
If the space-time geometrical impossibility of a radially out way is true, it should be implied that nothing (including light or whatever particle) can get out.
I feel like I'm missing something, or that many sources are either wrong or oversimplified.
So the question is: is any of those points of view more valid than the other? why?
Disclaimer: Not a physicist