Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard Schwarzschild solution with a curvature singularity at the center. Spherically symmetric collapse of matter in $\mathbb{ R}^4$ may result in these nonsingular black-hole solutions, if quantum-gravity effects allow for topology change near the center or if nontrivial topology is already present as a remnant from a quantum spacetime foam.
Categories: gr-qc hep-th