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Elsevier, Differential Geometry and its Applications, 1(24), p. 21-32, 2006

DOI: 10.1016/j.difgeo.2005.06.008

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On causality and closed geodesics of compact Lorentzian manifolds and static spacetimes

Journal article published in 2005 by Miguel Sánchez ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some natural topological assumptions (fulfilled, for example, if one of the conjugacy classes of deck transformations containing a closed timelike curve is finite) hold. As a consequence, any compact Lorentzian manifold conformal to a static spacetime is geodesically connected by causal geodesics, and admits a timelike closed geodesic. ; Comment: 18 pages, 1 figure, Latex, accepted in Diff. Geom. Appl