XLV.—The Internal and External Fields of a Particle in a Gravitational Field

Abstract

SummaryThe gravitational field of a system of particles was investigated by de Sitter as far back as 1916. A minor alteration to the analysis was made by Eddington and Clark in 1938. The amended value of the potential g44 is the same as that derived by Einstein, Infeld and Hoffmann without making use of the energy-tensor; this agreement suggests that the revised de Sitter argument is correct. In this paper we show that this is not the case, for the de Sitter analysis completely overlooked any possible interaction terms in the stress components of the energy-tensor. We find the value of these terms, pmn, and show that the agreement mentioned above is due to the fact that the volume integral of pu vanishes.