A Newtonian description of the geometry around a rotating black hole

Abstract

We suggest that most of the relevant properties of the Kerr space-time could be retrieved by suitably choosing a scalar potential which we present here. This potential can be used in the same manner as one uses the gravitational potential in Newtonian flat space-time. We present examples using both the general relativistic equations and our potential. The examples include test-particle motion and fluid motion around a Kerr black hole, as well as the evolution of the ellipticity of a self-gravitating, slowly rotating collapsing star.