How do we know for sure that the singularity inside black holes is infinitely dense?

Question

So what causes the black shell around black holes is the fact that light can't escape beyond that point. Since we can't see what is beyond a black hole's event horizon, how do we know for sure there is an infinitely dense singularity in it. Couldn't a black hole be a very dense "star" where the event horizon is located just above its surface?

Answer 1

That's a quite insightful question, because the straightforward and honest answer is that we don't know for sure what lies inside the event horizon. The "singularity" is a result of our math -- and to get the result of "infinite density", we divide by a radius of zero. You may remember that dividing by zero is, in general, considered a nonsensical no-no in math class. Thus, this particular prediction of our known physical laws is very troubling. What we can say is that if something prevents an infinite-density singularity inside the black hole, we don't know what that something is.

By the way, we've never seen a singularity anywhere -- all the predicted ones are inside event horizons of some sort. There's a hypothesis, the Cosmic Censorship Hypothesis, that claims singularities will always be surrounded by event horizons and never directly detected. The slightly silly name comes from the idea of a "naked singularity" that lacks an event horizon. People have theorized ways a naked singularity might exist, but they all involve unproven theories and cutting-edge astrophysics!