Closed timelike geodesics in compact spacetimes
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Abstract:
Let $M$ be a compact spacetime which admits a regular globally hyperbolic covering, and ${\mathcal C}$ a nontrivial free timelike homotopy class of closed timelike curves in $M.$ We prove that ${\mathcal C}$ contains a longest curve (which must be a closed timelike geodesic) if and only if the timelike injectivity radius of ${\mathcal C}$ is finite; i.e., ${\mathcal C}$ has a bounded length. As a consequence among others, we deduce that for a compact static spacetime there exists a closed timelike geodesic within every nontrivial free timelike homotopy class having a finite timelike injectivity radius.References
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Additional Information
- Mohammed Guediri
- Affiliation: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
- Email: mguediri@ksu.edu.sa
- Received by editor(s): March 16, 2005
- Published electronically: January 19, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 2663-2673
- MSC (2000): Primary 53C50, 53C22
- DOI: https://doi.org/10.1090/S0002-9947-07-04127-X
- MathSciNet review: 2286050