Revista Matemática Iberoamericana


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Volume 33, Issue 1, 2017, pp. 1–28
DOI: 10.4171/RMI/926

Published online: 2017-02-22

Connectivity by geodesics on globally hyperbolic spacetimes with a lightlike Killing vector field

Rossella Bartolo[1], Anna Maria Candela[2] and José Luis Flores[3]

(1) Politecnico di Bari, Italy
(2) Università degli Studi di Bari, Italy
(3) Universidad de Málaga, Spain

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.

Keywords: Lightlike vector field, global hyperbolicity, geodesic connectedness, Killing vector field, Cauchy hypersurface, stationary spacetime, gravitational wave, generalized plane wave

Bartolo Rossella, Candela Anna Maria, Flores José Luis: Connectivity by geodesics on globally hyperbolic spacetimes with a lightlike Killing vector field. Rev. Mat. Iberoam. 33 (2017), 1-28. doi: 10.4171/RMI/926