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Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids
Authors:A M Msomi  K S Govinder and S D Maharaj
Institution:(1) Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa;(2) Department of Mathematical Sciences, Mangosuthu University of Technology, P.O. Box 12363, Jacobs, 4026, South Africa;
Abstract:We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.
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