  The Einstein field equations have no known and acceptable interior solution
that can be matched to an exterior Kerr field. In particular, there are no
interior solutions that could represent objects like the Earth or other rigidly
rotating astronomical bodies. It is shown here that there exist closed surfaces
upon which the frame-dragging angular velocity and the red-shift factor for the
Kerr metric are constant. These surfaces could serve as a boundary between
rigidly rotating sources for the Kerr metric and the Kerr external field.
