On the stability of electrostatics stars with modified non-gauge invariant Einstein-Maxwell gravity

We use a modified Einstein-Maxwell gravity to study stability of an electrostatic spherical star. Correction terms in this model are scalers which are made from contraction of Ricci tensor and electromagnetic vector potential. Our motivation to use this kind of exotic EM gravity is inevitable influence of cosmic magnetic field in inflation of the universe which is observed now but its intensity suppresses in the usual gauge invariant EM gravity. In this work we use dynamical systems approach to obtain stability conditions of such a star and investigation of affects of interaction parts of the model on the stability.