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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Closed timelike geodesics in compact spacetimes


Author: Mohammed Guediri
Journal: Trans. Amer. Math. Soc. 359 (2007), 2663-2673
MSC (2000): Primary 53C50, 53C22
Published electronically: January 19, 2007
MathSciNet review: 2286050
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04127-X
PII: S 0002-9947(07)04127-X
Received by editor(s): March 16, 2005
Published electronically: January 19, 2007
Article copyright: © Copyright 2007 American Mathematical Society