dirac stars stability and modified einstein-dirac-maxwell gravity

To consider the cosmic magnetic effects on the rate of cosmic inflation, instead of unknown dark sector of matter/energy, some authors presented non-minimally coupled exotic einstein-maxwell (em) gravity theories which we address in this work. we  use one of these models and add dirac action functional interacting with gauge maxwell field to the exotic em gravity and then investigate the formation and stability of a relativistic fermion star by using the dynamical system approach. mathematical calculations predict important role of frequencies of the dirac waves in formation of the dirac star and whose critical energy density. dirac star is a particular kind of fermionic relativistic star which has spherically symmetric static metric field. in this context, the directional interaction parameter between the gravity, and the electromagnetic fields play more important role, particularly in size of the star. large values of that parameter  makes larger dirac star.  furthermore, we apply the dynamical system approach to find stabilization conditions of the dirac star. these conditions are linked to specific values of the total angular momentum quantum numbers (including both spin and orbital contributions).