Compact stars in the non-minimally coupled electromagnetic fields to gravity

We investigate the gravitational models with the non-minimal Y(R)F² coupled electromagnetic fields to gravity, in order to describe charged compact stars, where Y(R) denotes a function of the Ricci curvature scalar R and F² denotes the Maxwell invariant term. We determine two parameter family of exact spherically symmetric static solutions and the corresponding non-minimal model without assuming any relation between energy density of matter and pressure. We give the mass-radius, electric charge-radius ratios and surface gravitational redshift which are obtained by the boundary conditions. We reach a wide range of possibilities for the parameters k and α in these solutions. Lastly we show that the models can describe the compact stars even in the more simple case α =3 .