The Kerr solution for empty space-time is presented in an ellipsoidally
symmetric coordinate system and it is used to produce generalised ellipsoidal
metrics appropriate for the generation of rotating interior solutions of
Einstein's equations. It is shown that these solutions are the familiar static
perfect fluid cases commonly derived in curvature coordinates but now endowed
with rotation. The resulting solutions are also discussed in the context of
T-solutions of Einstein's equations and the vacuum T-solution outside a
rotating source is presented. The interior source for these solutions is shown
not to be a perfect fluid but rather an anisotropic three component perfect
fluid for which the energy momentum tensor is derived. The Schwarzschild
interior solution is given as an example of the approach.Comment: 14 page
