modified gauge invariant einstein-maxwell gravity and stability of spherical perfect fluid stars with magnetic monopoles

As an alternative gravity model, we consider an extended einstein-maxwell gravity containing a gauge invariance property. an extension is assumed to be an addition of a directional coupling between spatial electromagnetic fields with the ricci tensor. we will see importance of the additional term in making a compact stellar object and the value of its radius. as an application of this model we substitute ansatz of the magnetic field of a hypothetical magnetic monopole which has just time independent radial component and for matter part we assume a perfect fluid stress tensor. to obtain spherically symmetric internal metric of the perfect fluid stellar compact object we solve the tolman-oppenheimer-volkoff equation with a polytropic form of equation of state as p(ρ) = aρ2. using dynamical system approach we study stability of the solutions for which arrow diagrams show saddle (quasi stable) for a < 0 (dark stars) and sink (stable) for a > 0 (normal visible stars). we check also the energy conditions, speed of sound and harrison-zeldovich-novikov static stability criterion for obtained solution and confirm that they make stable state.