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

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.

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

References in corpus (2)

• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics