The complexification of a nonrotating sphere: An extension of the Newman–Janis algorithm

A procedure given by Newman and Janis, to obtain the exterior Kerr metric from the exterior Schwarzschild metric by performing a complex coordinate transformation, is applied to an interior spherically symmetric metric. The resulting metric can be matched to the exterior Kerr metric on the boundary of the source which is chosen to be an oblate spheroid. A specific example of an interior solution for which the energy density is positive is given in detail.