Lie Symmetries for a Conformally Flat Radiating Star
Abstract
We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial differential equation. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. We identify new categories of exact solutions to the boundary conditions. Two classes of solutions are of interest. The first class depends on a self similar variable. The second class is separable in the spacetime variables.
 Publication:

International Journal of Theoretical Physics
 Pub Date:
 September 2013
 DOI:
 10.1007/s1077301316205
 Bibcode:
 2013IJTP...52.3244A
 Keywords:

 Lie symmetries;
 Radiating stars;
 Heat flux