Topological holes in space-time

The solution of Einstein's field equations on a manifold with a topological hole in the 3-geometry is considered. It is found that such a hole is repelled by ordinary matter and behaves as if it had negative gravitational mass and positive inertial mass even though it has no actual energy content. Topological holes do not radiate or absorb energy if placed in a thermal bath of particles and radiation and are thus rather benign objects. They represent spaces which are null-geodesic incomplete ande hence singular. However, they are not more singular than the white holes forced upon us by quantum gravity. Since topological holes interact only gravitationally, they are difficult to observe