Generalized Euclidean stars with equation of state
Abstract
We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and find the Lie algebra corresponding to the optimal system of the symmetries. The symmetries in the optimal system allow us to transform the boundary condition to ordinary differential equations. The various cases for which the resulting systems of equations can be solved are identified. For each of these cases the boundary condition is integrated and the gravitational potentials are found explicitly. A particular group invariant solution produces a class of models which contains Euclidean stars as a special case. Our generalized model satisfies a linear equation of state in general. We thus establish a group theoretic basis for our generalized model with an equation of state. By considering a particular example we show that the weak, dominant and strong energy conditions are satisfied.
 Publication:

General Relativity and Gravitation
 Pub Date:
 May 2014
 DOI:
 10.1007/s107140141733z
 arXiv:
 arXiv:1412.8117
 Bibcode:
 2014GReGr..46.1733A
 Keywords:

 Radiating stars;
 Junction conditions;
 Equation of state;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, Submitted for publication