Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic Functions defined on the interval [0,1], These soluti ons are introduced by a suitable limiting process of Backlund transformatio ns applied to seed solutions of the Weyl class. It turns out that this clas s of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous tran sition to some Newtonian disk exists. It will be shown how for given bounda ry conditions (i.e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above sol utions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks po ssessing two spatially separated ergoregions.