Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606734 | Differential Geometry and its Applications | 2006 | 12 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Miguel Sánchez,