Very little that I know about general relativity is that there are solutions of its equations with singularities, and these are interpreted as black holes.
Mathematically, the most widespread kind of singularities are poles - e. g., for a single complex variable, if $z$ is a coordinate in the vicinity of the singularity, something like $1/z^n$ for $n=1,2,3,...$
Are the singularities of general relativity like that? There are singular points of different kind like $\sqrt z$ which make branching inevitable. Physically this would mean that orbiting around such point you could get to different sheets of the spacetime. Or, if it is $\log z$ or something even more nasty, the branching might be infinite, and interconnections between the sheets might be quite complicated.
Does such kind of spacetime branching occur? What is the physical meaning of its presence or absence?