The static two body problem

Abstract The problem of whether there exist static solutions of Einstein's equations for two extended bodies surrounded by vacuum is investigated. Equilibrium conditions for the general static situation are derived and their physical meaning discussed. Special cases of the problem are solved by using these equilibrium conditions. In one of these cases, the essential assumptions are that the space time is axisymmetric and that the matter of which the two bodies are composed consists of perfect fluid. Solu tions are also obtained in which these restrictions are weakened.