Einstein's Equations as a Dynamical System

Cornell University, Ithaca NY

Investigators

Abstract

This research in mathematical and computational gravitation seeks to make Einstein's equations more useful for observations of the cosmos which will be coming to us within the next decade. Professor York will focus on the study of formulations of the Einstein evolution equations that are mathematically rigorous and useful for large-scale numerical implementation and for systematic analytic approximation. There are also significant improvements in the initial-value equations, the canonical action principle, and the Bianchi identities. This work will exploit the methods of hyperbolic partial differential equations from the mathematical literature, generalized so as to apply to Einstein's theory. Development of certain fundamental concepts required for the existence of a rational general-relativistic statistical thermodynamics will also be studied. There exists tremendous scope for advances in understanding and practical use of gravity theory, matching those in experimental and observational gravity and cosmology that have been, are, and will be continuing to occur. It is such theory that this research will continue to find, to exhibit clearly, and to put to work in the next several years and beyond.