On the existence of rotating stars in general relativity

The Newtonian equations of motion, and Newton's law of gravitation can be obtained by a limit of Einstein's equations. For a sufficiently small constant the existence of a set of solutions (0) of Einstein's equations of a stationary, axisymmetric star is proven. This existence is proven in weighted Sobolev spaces with the implicit function theorem. Since the value of the causality constant depends only on the units used to measure the velocity, the existence of a solution for any small is physically interesting.