Topology change in classical and quantum gravity

Abstract

In a first-order formulation, the equations of general relativity remain well defined even in the limit that the metric becomes degenerate. It is shown that there exist smooth solutions to these equations on manifolds in which the topology of space changes. The metric becomes degenerate on a set of measure zero, but the curvature remains bounded. Thus if degenerate metrics play any role in quantum gravity, topology change is unavoidable.