Rapidly rotating general relativistic stars - I

The Newtonian self-consistent field method has been generalized 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. (author)