Radiation fluid stars in the non-minimally coupled Y(R)F^2 gravity

Abstract

We propose a non-minimally coupled gravity model in Y(R)F^2 form to describe the radiation fluid stars which have the radiative equation of state between the energy density rho and the pressure p given by 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 in differential form notation taking the infinitesimal variations of the model. We look for electrically charged star solutions to the field equations under the constraint eliminating complexity of the higher order terms in the field equations. We determine the non-minimally coupled function Y(R) and the corresponding model which admits new exact solutions in the interior of the star and the Reissner–Nordstrom solution at the exterior region. Using the vanishing pressure condition at the boundary together with the continuity conditions of the metric functions and the electric charge, we find the mass–radius ratio, charge–radius ratio, and the gravitational surface redshift depending on the parameter of the model for the radiation fluid star. We derive general restrictions for the ratios and redshift of the charged compact stars. We obtain 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 standard general relativistic stars.