Compact Lorentzian Manifolds Research Articles

Closed timelike geodesics

It is shown that every stable free t t -homotopy class of closed timelike curves in a compact Lorentzian manifold contains a longest curve which must be a closed timelike geodesic. This result enables one to obtain a Lorentzian analogue of a classical theorem of Synge. A criterion for stability is presented, and a theorem of Tipler is derived as a special case of the result stated above.

Extension of a compact Lorentz manifold

For a certain geodesically incomplete, compact Lorentz manifold T, we construct an analytic non-Hausdorff extension in which no geodesic bifurcates. The extension is geodesically incomplete, but is a maximal analytic Lorentz manifold in the sense that any further analytic extension has bifurcating geodesics. We also obtain a maximal analytic Hausdorff extension of the universal covering space of T. The latter extension is geodesically complete.