Generalized Raychaudhuri's equation for null hypersurfaces

Abstract

Black hole kinematics and laws governing their event horizonsin spacetimes are usually based on the expansion properties of families ofnull geodesics which generate such horizons. Raychaudhuri's equation is one of the most important tools in investigating the evolution of such geodesics. In this paper, we use the so-called Newton transformations to give a generalized vorticity-free Raychaudhuri's equation (Theorem $3.1$), with a corresponding null global splitting theorem (Theorem $3.5$) for null hypersurfaces in Lorentzian spacetimes. Two supporting physical models are also given.