On causality and closed geodesics of compact Lorentzian manifolds and static spacetimes |
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Authors: | Miguel Sá nchez |
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Affiliation: | Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain |
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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. |
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Keywords: | 53C50 53C22 58E10 |
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