Timelike topological feature
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No closed timelike curve (CTC) on a Lorentzian manifold can be continuously deformed as a CTC to a point, because Lorentzian manifolds are locally causally well-behaved. Every CTC must pass through some topological feature which prevents it from being deformed to a point. A test particle free falling along a closed timelike geodesic transits this feature; in the test particle's frame, the feature propagates toward the test particle. This features resembles a glider in Conway's Game of Life, but in a continuous spatial automaton rather than a (discrete) cellular automaton.
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