Stellar models with generalized polytropic equation of state

We find new classes of exact solutions to the Einstein field equations where the matter distribution satisfies a generalized polytropic equation of state. The matter distribution is uncharged with anisotropic pressures. Equations of state for polytropes and quark matter are contained as special cases. The matter variables and metric potentials can be obtained explicitly. Known solutions, for the choice of the gravitational potential made in this analysis, arise as special cases for particular choice of the equation of state parameters. A detailed physical analysis indicates that the model is well behaved.