  We consider the self-collision of portals in classical general relativity.
Portals are wormholes supported by a single loop of negative mass cosmic
string, and being wormholes, portals have a nontrivial topology. Portals can be
constructed so that the curvature is zero everywhere outside the cosmic string,
with vanishing ADM mass. The conical singularities of these wormholes can be
smoothed, yielding a spatial topology of $S^2 \times S^1$ with a point
corresponding to spatial infinity removed. If one attempts to collide the
mouths of a smoothed portal to induce self-annihilation, one naively might
think that a Euclidean topology is recovered, which would violate the classical
no topology change theorems. We consider a particular limit of smoothed portals
supported by an anisotropic fluid, and find that while the portal mouths do not
experience an acceleration as they are brought close together, a curvature
singularity forms in the limit that the separation distance vanishes. We find
that in general relativity, the interaction between portal mouths is not
primarily gravitational in nature, but depends critically on matter
interactions.
