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.
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