We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalizes the Mak-Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the center.

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface {t = constant} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be G. L. Leach, J. Math. Phys. 37, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter K to the electromagnetic field.

We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein-Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with variable, rational coefficients. In an earlier treatment this condition was integrated by first transforming it to a hypergeometric equation. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein-Maxwell system both in the form of special functions and elementary functions.Our results contain particular solutions found previously including models of charged relativistic spheres and uncharged neutron star models. *