Time, Closed Timelike Curves and Causality

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General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. These apparently violate causality, producing time-travel paradoxes. We shall briefly discuss these geometries and analyze some of their physical aspects.
8 pages, LaTeX2e, Kluwer Academic style files-included. Invited talk at the NATO Advanced Research Workshop, The Nature of Time: Geometry, Physics and Perception, May 21-24, 2002, Tatranska Lomnica, Slovak Republic. Revised version

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