Editorial note to: J. L. Synge, On the deviation of geodesics and null geodesics, particularly in relation to the properties of spaces of constant curvature and indefinite line-element and to: F. A. E. Pirani, On the physical significance of the Riemann tensor

Abstract

1. The papers by J. L. Synge and F. A. E. Pirani reprinted here played a major role in the understanding of the subtle relations between the geometrical and physical aspects of General Relativity Theory. Both papers make use of the equation of geodetic deviation. Synge’s paper [1], published in 1934 in the prestigious Annals of Mathematics, is the first publication where deviation of null geodesics is considered. A new result presented there consists in showing how the geodetic deviation equation can be used to obtain a new characterization of the sectional curvature in a (pseudo) Riemannian space (M,g). The equation is solved in spaces of constant curvature with g of Lorentzian signature ( +−− −) and used to analyze the global properties of these de Sitter and anti-de Sitter spaces. The exposition in Synge’s paper is so concise and lucid that it does not require any summary or additional comments. Most of its results have been incorporated into the book [2]. Global properties of the de Sitter space are thoroughly discussed in [3].