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We propose a non-minimally coupled gravity model in $ Y(R)F^2 $ form todescribe the radiation fluid stars which have the radiative equation of statebetween the energy density $ \rho $ and the pressure $p$ as $\rho=3p $. Here$F^2$ is the Maxwell invariant and $Y(R)$ is a function of the Ricci scalar$R$. We give the gravitational and electromagnetic field equations indifferential form notation taking the infinitesimal variations of the model. Welook for electrically charged star solutions to the field equations under aconstraint which eliminating complexity of the higher order terms in the fieldequations. We determine the non-minimally coupled function $Y(R)$ and thecorresponding model which admits new exact solutions in the interior of starand Reissner-Nordstrom solution at the exterior region. Using vanishingpressure condition at the boundary together with the continuity conditions ofthe metric functions and the electric charge, we find the mass-radius ratio,charge-radius ratio and gravitational surface redshift depending on theparameter of the model for the radiation fluid star. We derive generalrestrictions for the ratios and redshift of the charged compact stars. Weobtain a slightly smaller upper mass-radius ratio limit than the Buchdahl bound$ 4/9 $ and a smaller upper redshift limit than the bound of the standardGeneral Relativistic stars.

Radiation Fluid Stars in the Non-minimally Coupled $Y(R)F^2$ Gravity