The problem of <i>n</i> bodies in general relativity theory

Abstract

Abstract 1. In a recent investigation of the problem of two bodies in general relativity theory, Prof. Levi-Civita (1937b) has reached the conclusion that the centre of gravity has a secular acceleration in the direction of the major axis of the orbit towards the periastron of the larger mass. He gives an example of a binary star in which this acceleration may become detectable in much less than a century, perhaps even in a few years. Since the periastron slowly revolves, Levi-Civita’s result implies that the binary star as a whole spontaneously describes a circle of very large radius. There seems to be no obvious ground for regarding this as impossible; it is conceivable that an unsymmetrical system may radiate momentum by gravitational waves and so experience a recoil. But the behaviour is so peculiar as to inspire doubt; and we determined to re-examine the problem with a view either to detecting an error or to obtaining further light on the nature of the phenomenon.