MATEMATIČKI VESNIK Vol. 70, No. 1, pp. 79–88 (2018) 

Generalized Raychaudhuri’s equation for null hypersurfacesF. Massamba and S. SsekajjaDSchool of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Private Bag X01, Scottsville 3209, South Africa Email: massfort@yahoo.fr, Massamba@ukzn.ac.za and School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Private Bag X01, Scottsville 3209, South Africa Email: ssekajja.samuel.buwaga@aimssenegal.orgAbstract: 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 socalled Newton transformations to give a generalized vorticityfree Raychaudhuri’s equation (Theorem $3\xb71$), with a corresponding null global splitting theorem (Theorem $3\xb75$) 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Dec 2017. This page was last modified: 11 Mai 2018.
© 2017 Mathematical Society of Serbia (Društvo matematičara Srbije)
