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

Massamba, Fortuné; Ssekajja, Samuel

Mat. Vesn. 70, No. 1, 79-88 (2018).

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.

MSC:

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

Keywords:

null hypersurfaces; null horizons; Newton tranformations; mean curvature; black hole

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