  The increasing interest in compact astrophysical objects (neutron stars,
binaries, galactic black holes) has stimulated the search for rigorous methods,
which allow a systematic general relativistic description of such objects. This
paper is meant to demonstrate the use of the inverse scattering method, which
allows, in particular cases, the treatment of rotating body problems. The idea
is to replace the investigation of the matter region of a rotating body by the
formulation of boundary values along the surface of the body. In this way we
construct solutions describing rotating black holes and disks of dust
("galaxies"). Physical properties of the solutions and consequences of the
approach are discussed. Among other things, the balance problem for two black
holes can be tackled.
