Exact solutions for compact stars in general relativity

Complete, exact, analytic solutions to the spherically symmetric Einstein equations have been constructed. Beginning with the Tolman VII solution we first \complete" the solution by computing an expression for the pressure and subsequently the equation of state. The Tolman VII solution is then extended to include non-zero mass densities at the fluid-vacuum interface. The method developed to construct these solutions is extended to include transverse pressures and charge. Furthermore the quadratic density profile of the Tolman VII type solutions is modified to include quartic density profiles that lead to expressions in terms of Jacobi elliptic integrals. It is shown that, depending on the outer boundary conditions placed on the mass density, the equations of state lead to either a set of polytropes or behaviour that mimics strange quark matter.