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.