General relativity, partial differential equations, and dynamical systems

Fischer, A. E. and J. E. Marsden

Proc. Sympos. Pure Math., 23, (1973), 309-327

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.