The causal boundary of the trousers space

Abstract

The authors study a smooth flat two-dimensional spacetime whose spacelike sections change topology; the problematic 'point of topology change' is excluded from the manifold. The causal boundary construction inserts this point back into the manifold. The result is again a smooth manifold, but neither the Lorentz metric nor the Levi-Civita connection extend to the new point; in fact, the causal structure at the new point is not that of a Lorentz manifold. All these results continue to hold for all metrics sufficiently close to the flat metric.