Null hypersurfaces in Brinkman spacetimes

Abstract

We study normalized null hypersurfaces in Brinkmann spacetimes with special attention paid to Plane Fronted Waves. We explore geodesibil- ity criterion and characterization for null hypersurfaces in links with relative position of a global parallel null vector field or under relative harmonicity con- dition on the local H−factor of the P F W −metric. We prove that there is no compact null hypersurfaces in Plane Fronted Waves for which the local H−factor has sign. We point out that Lorentzian Einstein manifolds with non zero cosmology constant admit no global parallel null vector field, and the same is for Lorentzian space forms with non zero sectional curvature. We establish sufficient conditions for the unicity up to constant factor of parallel null vector field.