Abstract
We construct the disk sources matched to the exact vacuum Kerr and to the two classes of Tomimatsu-Sato spacetimes. We analyze two models of the matter forming these disks.
At each radius we consider either a rotating massive ring with pressure or two counter-rotating streams of particles in circular geodesic motion. Dragging effects present in such spacetimes lead either to the rotation of rings or the asymmetry between streams.
We demonstrate that the model of rotating rings is general enough to describe all axisymmetric stationary disk sources with vanishing radial pressure which satisfy the weak energy condition, and that centrifugal effects present in the disk sources of spacetimes with large angular momentum prevent the construction of highly compact sources made of counter-rotating streams of geodesic particles. We illustrate the radial distribution of the mass inside the disks and the angular velocities of both geodesic streams.