Topology and Closed Timelike Curves II: Causal structure

Details Topology and Closed Timelike Curves II: Causal structure Topology and Closed Timelike Curves II: Causal structure

2006-07-31

arxiv.org/abs/gr-qc/0607134v5

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

See companion paper by the same title

Scientific paper

Because no closed timelike curve (CTC) on a Lorentzian manifold can be deformed to a point, any such manifold containing a CTC must have a topological feature, to be called a timelike wormhole, that prevents the CTC from being deformed to a point. If all wormholes have horizons, which typically seems to be the case in space-times without exotic matter, then each CTC must transit some timelike wormhole's horizon. Therefore, a Lorentzian manifold containing a CTC may nevertheless be causally well behaving once its horizon's are deleted. For instance, there may be a Cauchy-like surface through which every timelike curve passes one and only once before crossing a horizon.

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