A model of the reissner-nordstrom interior source

A new exact static interior solution of the Einstein equations for a gravitating ball filling with neutral and charged fluids is obtained by the Darboux method. The solution is an extension of the earlier solution of charged ball with mass density’s describing by a polynomial function of tenth order. This solution describes compact astrophysical objects with electric charge. It is shown that a behavior of the total energy density’s distribution of generalised solution nearby the ball center can be described as the cusp catastrophe.