Kerr Metric, Rotating Sources, and Machian Effects

In a recent paper, the author gave a recipe for constructing exact interior solutions which might serve as sources of the Kerr metric. Here the recipe is given again, but in simpler form, and an example of an interior solution is given in detail. Some properties of these solutions are discussed, including the shape, mass density, and rotation rates of the bodies described. It is proven that solutions of this type exist which describe uniformly rotating bodies at least up to second order in the angular momentum parameter $b$. In the final section, a discussion is given which indicates that strong gravitational fields plus high-rotational velocities can lead to correspondingly high-rotational inertial effects on the observer who is near or inside the body. These inertial effects also give some direct information about the rotation of the body. This enables us to prove that uniformly rotating rings of mass could not serve as sources of the Kerr metric.