Whitehead's Law of Gravitation in a Space-Time of Constant Curvature

Abstract

A generalization of Whitehead's law of gravitation for a discrete set of particles having arbitrary world-lines in a flat background space-time is formulated for a space-time of constant curvature. It is then extended by a method of Synge (Rayner 1954) to include systems having finite and continuous proper-density and velocity distributions. The new law is particularly adapted to a cosmological theory like that previously considered by the author in which every gravitating particle recedes with uniform velocity from a common spatio-temporal origin.