Compact Stars in the Non-minimally Coupled Electromagnetic Fields to Gravity

We investigate the gravitational models with the non-minimal $Y(R)F^2$ 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 $F^2$ 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 $\alpha$ in these solutions. Lastly we show that the models can describe the compact stars even in the the more simple case $\alpha=3$.