Taking a globally hyperbolic spacetime endowed with a complete lightlike Killing vector field and a complete Cauchy hypersurface, we characterize the points which can be connected by geodesics. A straightforward consequence is the geodesic connectedness of globally hyperbolic generalized plane waves with a complete Cauchy hypersurface.
Cite this article
Rossella Bartolo, Anna Maria Candela, José Luis Flores Dorado, Connectivity by geodesics on globally hyperbolic spacetimes with a lightlike Killing vector field. Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 1–28DOI 10.4171/RMI/926