# On the existence of geodesics on globally hyperbolic spacetimes with a lightlike Killing vector field

## By Rosella Bartolo (Politecnico di Bari)

Given 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.

References

[1] R. Bartolo, A.M. Candela, J.L. Flores: Connection by geodesics on globally hyperbolic spacetimes with a lightlike Killing vector field. arXiv:1405.0804[math.DG], (2014).

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