  The two known exact solutions of Einstein's field equations describing
rotating objects of physical significance - a black hole and a rigidly rotating
disk of dust - are discussed using a single mathematical framework related to
Jacobi's inversion problem. Both solutions can be represented in such a form
that they differ in the choice of a complex parameter and a real solution of
the axisymmetric Laplace equation only. A recently found family of solutions
describing differentially rotating disks of dust fits into the same scheme.
