Understanding the Singularity of Black Holes

Question

Could someone please explain how we know the singularity has an infinite density and zero size/volume? From reading around online black holes have a defined radius (the event horizon) but this isn't its true size, it's just a reference point. If a supermassive star is so large that neuron degeneracy pressure cannot halt the collapse then it turns into a black hole. But I don't see how scientists know it has zero size? They say the mass is in a volume smaller than an electron but how do they know this? How do they know all the massive at the singularity isn't in some tiny (but finite) volume?

Answer 1

The singularity arises as a solution from Einstein's field equations.However singularities in physics is a red flag that we push to its limit the theory which predicts the singularity.As closer as we get to the center of a black hole,the more quantum effects start to dominate.However we dont have a theory of quantum gravity to tell us what will happen there.And even if we did physics isnt math we need physical evidence to support a theory and since past the event horizon that part of the universe is forever inaccessible to us we may never confirm the truth.However in the future if we manage to create tiny black holes in particle accelerators and study these tiny black holes maybe we can have a very good guess on what is happening past the event horizon of a stellar or bigger black hole.

Answer 2

Could someone please explain how we know the singularity has an infinite density and zero size/volume ?

We don't. We cannot observe anything beyond the event horizon. All we can say is that if the theory of general relativity continues to apply everywhere inside the event horizon then there will be a singularity at the centre of the black hole (this is a consequence of the Penrose-Hawking singularity theorems). However, a singularity appears to be a non-physical outcome. This is one of the reasons why physicists believe that general relativity must break down at some point inside a black hole - but we don't yet have a viable theory of quantum gravity to replace it.