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

Authors
Journal
Differential Geometry and its Applications
0926-2245
Publisher
Elsevier
Publication Date
Volume
24
Issue
1
Identifiers
DOI: 10.1016/j.difgeo.2005.06.008
Keywords
  • Closed Geodesic
  • Geodesic Connectedness
  • Static And Stationary Spacetimes
  • Causality
  • Totally Vicious
  • Timelike Geodesic
  • Lorentzian Manifolds
Disciplines
  • Earth Science
  • Mathematics
  • Physics

Abstract

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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