New charged shear-free relativistic models with heat flux
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We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein–Maxwell system is governed by the generalised pressure isotropy condition which contains a contribution from the electric field. This condition is a highly nonlinear partial differential equation. We analyse this master equation using Lie’s group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. The first generator is independent of the electromagnetic field. The second generator depends critically on the form of the charge, which is determined explicitly in general. We provide exact solutions to the gravitational potentials using the symmetries admitted by the equation. Our new exact solutions contain earlier results without charge. We show that other charged solutions, related to the Lie symmetries, may be generated using the algorithm of Deng. This leads to new classes of charged Deng models which are generalisations of conformally flat metrics.
KeywordsMaster Equation Gravitational Potential Gravitational Collapse Order Differential Equation Stellar Model
YN, KSG and SDM wish to thank the National Research Foundation and the University of KwaZulu-Natal for support. SDM acknowledges that this work is based on research supported by the South African Research Chair Initiative of the Department of Science and Technology and the National Research Foundation.
- 32.S. Dimas, D. Tsoubelis, in Proceedings of the 10th International Conference in Modern Group Analysis, University of Cyprus, Larnaca (2005) Google Scholar