Somewhat OT, but I've had this question for a while now: Why do we know that black holes have a singularity? This might be a dumb question, but when you increase the mass of, let's say, a neutron star, at some point gravitaton is too strong for light to escape and there'll be a Schwarzschild border. But why does the mass inside of a black hole have to shrink to a singularity? Can't there be some ultra-dense but finitely small core?
Essentially the Schwarzschild equations based off relativity say that happens.
The problem turns out that we have no way to actually know if that's what happens at the core of the black hole. The event horizon presents a problem where it becomes impossible to experimentally test anything beyond that point. For example the fundamental constants could alter themselves inside the event horizon, as long as the event horizon was still a one way trip, it wouldn't matter, we'd not be able to gather any information about that.
If we assume general relativity is correct, then singularities are an unavoidable result of black holes. The math simply does not allow for such a large density to not form a singularity. Having said that, we know GR is not correct, as it fails to account for any quantum phenomena; and we have thus far been unable to combine GR and QFT into a unified theory. Attempts to combine the theories fall under the title of quantum gravity. Several proposed theories of quantum gravity predict that black hole singularities do not exist.
I'm not familiar with the current thinking about this, but last decade the singularity was understood as a gap in our understanding/model. Of course there's model dependent realism, after all if all you have are models (built on decades or centuries of data), with no means of devising new experiments, what else is reality?
As I understand it: before gravity captures light--which moves as fast as anything can move--gravity will have captured everything else and overcame all other repulsive forces crushing the matter into a singularity
edit: pixl97 made a really good point right as I posted. I should say "As I understand the math"
