A geometric flow on null hypersurfaces of Lorentzian manifolds

Abstract

We introduce a geometric flow on a screen integrable null hypersurface in terms of its local second fundamental form. We use it to give an alternative proof to the vorticity free Raychaudhuri’s equation for null hypersurface, as well as establishing conditions for the existence of constant mean curvature (CMC) null hypersurfaces, and leaves of constant scalar curvatures.

Keywords

• null hypersurface
• constant mean curvature
• raychaudhuri’s equation
• gradient soliton
• primary 53c25
• secondary 53c40, 53c50