Geodesic models generated by Lie symmetries
arXiv:1412.8111 · doi:10.1007/s10714-013-1650-6
Abstract
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.
16 pages, Submitted for publication
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- Similarity Inner Solutions for the Pulsar Equation
- Lie Symmetries, Painlevé analysis and global dynamics for the temporal equation of radiating stars