Gravitational waves

Abstract

IN THE SECOND “golden” decade of this century Albert Einstein unified physics and geometry and fulfilled a long cherished dream of Karl Friedrich Gauss, Bernhard Riemann and William K. Clifford. This geometrical theory of gravitation had “magnetic” types of velocity‐dependent forces and a finite velocity of gravitational interactions; it apparently predicted gravitational radiation. The equations describe gravitation in terms of the curvature of space‐time. Riemann gave the concept of the curvature of n‐dimensional space as a logical generalization of the concept of curvature of a two‐dimensional surface. Radii of curvature for such a surface are easy to visualize. There is a simple connection (given in the box on p. 39) between these radii and the sum of the angles of a small triangle made up of geodesic lines (figure 1).