Generalized Raychaudhuri’s equation for null hypersurfaces. (English) Zbl 1474.53268

Summary: Black hole kinematics and laws governing their event horizons in spacetimes are usually based on the expansion properties of families of null 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.


53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C80 Applications of global differential geometry to the sciences
83C57 Black holes
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