Doctoral thesis
We find new classes of exact solutions for the Einstein-Maxwell field equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are integrated by specifying forms for the measure of anisotropy and one of the gravitational potentials which are physically reasonable. A general feature of our models is that isotropic pressures are regained when certain parameters vanish; this behaviour is missing in most previous treatments. Particular models found in our results generalize the models of Mak and Harko, Komathiraj and Maharaj, Misner and Zapolsky, and the earlier results of Einstein. The graphical and physical analyses indicate that the gravitational potentials, the matter variables, the electric field and the mass are well behaved. In performing physical analysis we regain masses and radii of stellar objects consistent with observations. It is also shown that other masses and radii may be generated which are in acceptable ranges consistent with observed values of stellar objects. In particular we have established that our model is consistent with the stellar object SAXJ1808.4-3658. A study of the mass-radius relation indicates the effect of the electromagnetic field and anisotropy on the mass of the relativistic star.