Differentially rotating disks of dust

We present a three-parameter family of solutions to the stationary axisymme tric Einstein equations that describe differentially rotating disks of dust . They have been constructed by generalizing the Neugebauer-Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspon d to disks with angular velocities depending monotonically on the radial co ordinate; both decreasing and increasing behaviour is exhibited. In general , the solutions are related mathematically to Jacobi's inversion problem an d can be expressed in terms of Riemann theta functions. A particularly inte resting two-parameter subfamily represents Backlund transformations to appr opriate seed solutions of the Weyl class.