Causal Properties of Lorentzian Manifolds and Regular Coverings

Regular coverings of Lorentzian manifolds are studied under the assumption that the covering map is isometric and preserves time orientation. Conditions for the covering manifold are obtained that are necessary and sufficient for the base to be chronological, causal, strongly or stable causal, and also globally hyperbolic manifold. As a corollary, statements are obtained that the indicated causal properties rise from the base to the covering manifold. In the general situation the opposite is not true. The connections between splittings of the base and the covering manifold in the case of their global hyperbolicity are also studied.