2004/05/20 by F. I. Cooperstock, Cooperstock, F. I., S. Tieu +2
Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Model Reduction and Neural Networks #astro-ph #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.gr-qc/0405114
17 pages, 6 postscript figures
arxiv created 2004/05/20 · openalex publication_date 2004/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Examples are given of the creation of closed timelike curves by choices of coordinate identifications. Following Gödel's prescription, it is seen that flat spacetime can produce closed timelike curves with structure similar to that of Gödel. In this context, coordinate identifications rather than exotic gravitational effects of general relativity are shown to be the source of closed timelike curves. Removing the periodic time coordinate restriction, the modified Gödel family of curves is expressed in a form that retains the timelike and spacelike character of the coordinates. With these coordinates, the nature of the timelike curves is clarified. A helicoidal surface unifies the families of timelike, spacelike and null curves. In all of these, it is seen that as in ordinary flat spacetime, periodicity in the spatial position does not naturally carry over into closure in time. Thus, the original source of serious scientific speculation regarding time machines is seen to be misconceived.