Not all black holes have a curvature singularity at their center (an example). But in principle, I thought that the curvature singularity was a direct result of the fact that the mass is concentrated in a non-3D region (like a point, or a ring for a rotating black hole).
So how is it possible to have an infinite 3D-density but not a curvature singularity?
Where with this I mean that the "3D-density" is infinite because the mass is confined in a 2D/1D/0D region.
