On electrostatics in a gravitational field

Abstract

In a recent paper, Prof. Whittaker has discussed the effect, according to the general theory of relativity, of gravitation on electromagnetic phenomena. In particular, he has discussed electrostatics in gravitational fields of two kinds, namely (i) the field due to a single gravitating mass, in which case space-time has the metric discovered by Schwarzschild, and (ii) a limiting case of this, called a quasi-uniform field, in which the gravitational force is, in the neighbourhood of the origin, uniform. Whittaker’s general method, so far as electrostatical problems were concerned, was to solve the partial differential equation satisfied by the electrostatic potential in terms of generalised harmonic functions, and then, from these, to build up other solutions. In this way, he succeeded in finding an algebraic expression which represents the potential of a single electron in the quasi-uniform field; he did not, however, obtain a corresponding algebraic expression for the potential of an electron in the Schwarzschild field.