Static and isotropic gravitational fields

Abstract

The object of this Paper is to give a brief account of the principles of Einstein's General Theory of Relativity as applied to those problems in which they have received their most striking confirmation. To this end we have limited our investigations to the consideration of dynamical manifolds which are static and isotropic in character. It has then proved possible to abandon the notation and theory of the Absolute Differential Calculus, and to substitute in its place some classical theorems of Lord Kelvin and M. J. Liouville. Although the scope of these inquiries is not extensive, within the limits of our investigations we have explained the method of the construction and solution of Einstein's field equations, and have given the applications of these results to the problems of planetary motion and of the deviation of light rays in the solar gravitational field. At the same time we have endeavoured to make explicit the various assumptions involved in this theory.