Charged Polytropic Stars and a Generalization of Lane-Emden Equation
  In this paper we will discuss charged stars with polytropic equation of state, where we will try to derive an equation analogous to the Lane-Emden equation. We will assume that these stars are spherically symmetric, and the electric field have only the radial component. First we will review the field equations for such stars and then we will proceed with the analog of the Lane-Emden equation for a polytropic Newtonian fluid and their relativistic equivalent. These kind of equations are very interesting because they transform all the structure equations of the stars in a group of differential equations which are much more simple to solve than the source equations. These equations can be solved numerically for some boundary conditions and for some initial parameters. For this we will assume that the pressure caused by the electric field obeys a polytropic equation of state too. 
Rodrigo Picanco, Manuel Malheiro and Subharthi Ray