Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids
Abstract
We consider a radiating shearfree 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.
 Publication:

International Journal of Theoretical Physics
 Pub Date:
 April 2012
 DOI:
 10.1007/s1077301110056
 Bibcode:
 2012IJTP...51.1290M
 Keywords:

 Gravitating fluids;
 Symmetries;
 Higher dimensional physics