Rotating bodies as boundary value problems

There are physically interesting particular cases in which the treatment of the matter region of rotating bodies may be replaced by the formulation of boundary values along the surface of the body. In this way, rotating black holes and rotating disks of dust ("galaxies") are described by boundary value problems which can be solved by means of the so-called Inverse Scattering Method. 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.