Rapidly rotating general relativistic stars - I. Numerical method and its application to uniformly rotating polytropes

We have generalized the Newtonian self-consistent field method to a general relativistic case in order to obtain structures of rapidly rotating relativistic stars. It seems that this method is more powerful than other methods; for any strength of gravity, we can compute equilibrium states if they exist. For the sake of showing the power of this new method, we have computed uniformly rotating polytropic stars having polytropic indices N = 1/2, N = 3/2 and N = 3 for several choices of strength of gravity including the limiting case of strong gravity. Each computed sequence terminates at a critical point where the centrifugal force exactly balances the gravity at the equatorial surface. For strong gravity cases, the configurations of rotating stars look like Newtonian polytropes having much higher polytropic indices, because the mass is concentrated into the central region due to the strong gravity effect. For N = 3/2 and N = 3 models, this mass concentration is so large that the critical angular velocity is much smaller than that for Newtonian models having the same polytropic index. As a result, the gravitational mass cannot increase greatly for uniformly rotating configurations.