  Using exactly solvable models, it is shown that black hole singularities in
different electrically charged configurations can be cured. Our solutions
describe black hole space-times with a wormhole giving structure to the
otherwise point-like singularity. We show that geodesic completeness is
satisfied despite the existence of curvature divergences at the wormhole
throat. In some cases, physical observers can go through the wormhole and in
other cases the throat lies at an infinite affine distance.
