ABSTRACT
Good textbooks on Electrodynamics such as Jackson’s ‘Classical Electrodynamics’ start with four or five chapters on electrostatics and magnetostatics devoted to the time-independent fields of stationary sources. The main topic is the mathematical and physical discussion of the linear Poisson equation and, especially, the solution of the classical boundary value problems for that equation. No doubt, a corresponding procedure would be just as desirable for systematic representations of gravity. However, gravitostatics including stationary phenomena such as rotating bodies is a nonlinear theory from the very beginning. For a long time, no mathematical algorithm for a systematic treatment of its basic equations was known. The situation changed in 1978, when several authors (Maison 1978, Belinski and Zakharov 1978, Harrison 1978, Herlt 1978, Hoenselaers et al. 1979, Neugebauer 1979, 1980, Hauser and Ernst 1979, 1980, Alekseev 1980) discovered that Einstein’s vacuum equations for stationary and axially symmetric gravitational fields can be ‘linearized’ in terms of a ‘Linear Problem’ and solved by means of the so-called Inverse Scattering Method. This method even turned out to be the suitable instrument for tackling boundary value problems. Thus, the future book writers are equipped with some mathematical tools to formulate the chapters on gravitostatics. The following three lectures are meant to discuss some aspects of this project. In particular, we intend
