Outline of alternative approaches to particle solutions obeying Einstein's gravitation theory

Abstract

Two general approaches to a classical theory of charged particles are presented to emphasize the meaning of gravitation as geometry in a classical theory of charged systems. One approach is due to Wheeler's attempt to construct charge and mass without introducing sources anywhere. This so-called geometrodynamical aspect leads to a departure from Euclidean topology. The other approach, following Euclidean topology in a Riemannian space-time, constructs particle models having sources of charge and mass. Point particles of Born-Infeld type and particles with finite size are discussed. The influence of an empty space of constant curvature on charge and mass of an embedded charged particle is investigated. The aim of this paper is twofold; namely first to show that the Einstein-Maxwell theory admits various solutions describing classical charged particles and second to stress Einstein's point of view of identifying gravitation with geometry in contrast to the usual field theory (flat space-time approach), which is concerned with approximations. Particle models can be constructed only from the full nonlinearity of the theory. To this end the common statement that gravitation behaves like a weakly interacting field is found to be unsubstantiated.