A fifth order differential equation for charged perfect fluids
Abstract
We investigate the master nonlinear partial differential equation that governs the evolution of shearfree spherically symmetric charged fluids. We use an approach which has not been considered previously for the underlying equation in shearfree spherically symmetric spacetimes. We derive a fifth order purely differential equation that must be satisfied for the underlying equation to admit a Lie point symmetry. We then perform a comprehensive analysis of this equation utilising the Lie symmetry analysis and direct integration. This enables us to reduce the fifth order equation to quadratures. Earlier results are shown to be contained in our general treatment.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 March 2012
 DOI:
 10.1063/1.3694279
 arXiv:
 arXiv:1301.1411
 Bibcode:
 2012JMP....53c3707K
 Keywords:

 EinsteinMaxwell equations;
 Lie groups;
 master equation;
 nonlinear equations;
 partial differential equations;
 spacetime configurations;
 04.40.Nr;
 02.30.Jr;
 EinsteinMaxwell spacetimes spacetimes with fluids radiation or classical fields;
 Partial differential equations;
 General Relativity and Quantum Cosmology
 EPrint:
 17 pages, To appear in J. Math. Phys