Static spherically symmetric solutions in Einstein’s unified field theory

Abstract

A new static spherically symmetric solution of Einstein’s unified field equations is derived. Certain boundary conditions are applied to this solution and to those already known, and the nature of the resulting fields is investigated. The only solution in the magnetic case corresponds to a magnetic pole without mass. In the electric case all the solutions correspond to continuous charge distributions, and the fields tend asymptotically to that of a point charge in classical theory. Several of the solutions are singular at an infinity of values of r , the radial co-ordinate, and in these the charge density is not of constant sign; but there are two solutions which have no singularities for finite values of r greater than 2 m (where m is a constant associated with the mass), and in which the charge density has constant sign throughout the field.