General relativity partial differential equations and dynamical systems

Abstract

In this paper we study two aspects of the Einstein equations of evolution for an empty spacetime. In the first part (§§1-3) we give a simple direct proof that the differentiability of the Cauchy data is maintained for short time. In the second part (§§4-5) we sketch how, on a suitable configuration space. Einstein's equations can be considered as forced geodesics modified by terms which reflect a moving coordinate system equipped with its own system of clocks. Both of these topics will be presented in more detail in paper [15], [12] by Fischer and Marsden.