A Newtonian description of the geometry around a rotating black hole

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 Kerr black hole, as well as the evolution of the ellipticity of a self-gravitating slowly rotating collapsing star.