# What is the singularity of an actual collapsing black hole?

In most general relativity texts, the singularity is treated as a point removed from the manifold, to avoid having to deal with the infinite curvature of the Ricci scalar.

But in the case of a more realistic scenario (let's say a spherically symmetric collapse, for instance), does this idea really hold up? We start with a, let's say, (partial) Cauchy surface, with topology $\Bbb R^3$. The matter collapses, leading to a black hole. I'm not quite sure of the topology of a non-maximally extended black hole, especially one from stellar collapse (in particular I'm not sure if the singularity matters all that much since I have a suspiscion it might not affect the topology, as it may be at timelike infinity). If the topology of the spacelike hypersurface is of the form $\Bbb R^3 \setminus \{0\}$, does that not violate theorems on topology change? As I'm pretty sure it will not violate conditions of that theorem on time orientability or closed timelike curves, does the metric have a degenerate point?

I know that there are also ways to treat singularities without removing the point (ie with generalized functions), and that the problem probably doesn't happen in quantum gravity, but is it a problem when it comes to classical general relativity?

• You can't get a "realistic" singularity out of GR, which doesn't describe matter, it doesn't even describe spacetime, it only describes the distortion of spacetime by matter and the movement of that matter in its own distortion, but we don't even know up to what scale the theory is valid (and it's not clear there is a non-suicidal way of finding out). – CuriousOne May 31 '16 at 11:16
• Once again @CuriousOne has posted the answer in a comment. The fact that a singularity appears in the theory is more an indicator of a failure of the theory than it is an indicator of what the center of a black hole is like. Many theorists think there probably isn't a physical singularity. – Asher May 31 '16 at 12:41