Progress in relativistic gravitational theory using the inverse scattering method

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 article 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.