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

Miguel Sánchez
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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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Miguel Sánchez. 2005-02-15. On causality and closed geodesics of compact Lorentzian manifolds and static spacetimes. https://arxiv.org/abs/math/0502322

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