Introduction

One of the simplest situations for a bounded rotating source in Newtonian theory of gravitation is the case of a homogenous inviscid fluid mass rotating uniformly which was considered briefly in Section 1.1. In this case both the interior and exterior Newtonian gravitational potentials are known explicitly and this case has been studied extensively (see, for example, Chandrasekhar, 1969). In general relativity the finding of an exact solution of Einstein's equations which represents a uniformly rotating homogeneous inviscid fluid mass – either the interior or the exterior field – presents formidable problems and we are far from finding such an exact solution, if one exists. Some progress has been made for finding an approximate solution for this case (see, for example, Chandrasekhar, 1971, Bardeen, 1971). In general, finding exact solutions of Einstein's equations for well-defined physical situations is extremely difficult and very few such solutions are known. The gravitational field of a uniformly rotating bounded source must depend on at least two variables. Finding any solutions of Einstein's equations depending on two or more variables is quite difficult, let alone a physically interesting one. The first exact solution of Einstein's equations to be found which could represent the exterior field of a bounded rotating source was that of Kerr (1963). An essential property of such a solution is that it should be asymptotically flat, since the gravitational field tends to zero as one moves further and further away from the source.