A conformal Hopf-Rinow theorem for semi-Riemannian spacetimes
Authors: Annegret Burtscher
Summary: The well-known Hopf-Rinow Theorem states, amongst others, {that a} Riemannian manifold is metrically full if and solely whether it is geodesically full. The Clifton-Pohl torus fails to be geodesically full proving that this theorem can’t be generalized to compact Lorentzian manifolds. Alternatively, Hopf and Rinow characterised metric completeness additionally by properness. García-Heveling and the creator just lately obtained a Lorentzian completeness-compactness end result for open manifolds with an identical taste. On this manuscript, we lengthen the null distance used on this strategy and our theorem to correct cone constructions and to a brand new class of semi-Riemannian manifolds, dubbed (n−ν,ν)-spacetimes. Furthermore, we reveal that our end result implies, and therefore generalizes, the metric a part of the Hopf-Rinow Theorem.
