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

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

2005-02-15

arxiv.org/abs/math/0502322v1

Diff. Geom. Appl. 24 (2006) 21--32

Mathematics

Differential Geometry

18 pages, 1 figure, Latex, accepted in Diff. Geom. Appl

Scientific paper

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.

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