EMIS ELibM Electronic Journals MATEMATIČKI VESNIK
Vol. 70, No. 1, pp. 79–88 (2018)

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Generalized Raychaudhuri’s equation for null hypersurfaces

F. Massamba and S. Ssekajja

DSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, South Africa E-mail: massfort@yahoo.fr, Massamba@ukzn.ac.za and School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, South Africa E-mail: ssekajja.samuel.buwaga@aims-senegal.org

Abstract: 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.

Keywords: Null hypersurfaces; null horizons; Newton tranformations; mean curvature; black hole.

Classification (MSC2000): 53C42; 53C50, 53C80

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