This research in mathematical gravitation seeks to make Einstein's equations more useful for numerical simulations of phenomena that may soon be observed by gravitational wave detectors. It 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.
