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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 rotation of
rings or asymmetry of both 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 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.