Einstein's Equations as a Dynamical System

这项在数学和计算引力方面的研究试图使爱因斯坦的方程式在未来十年内对我们即将到来的宇宙的观测更加有用。约克教授将专注于研究爱因斯坦演化方程的公式，这些公式在数学上是严格的，对于大规模的数值实施和系统的解析近似是有用的。在初值方程、正则作用量原理和比安奇恒等式方面也有显著的改进。这项工作将利用数学文献中的双曲偏微分方程组的方法，推广到爱因斯坦的理论中。还将研究理性广义相对论统计热力学存在所需的某些基本概念的发展。在对引力理论的理解和实际应用方面，存在着巨大的进步空间，可以与已经、现在和将继续发生的实验和观测重力和宇宙学相媲美。正是这样的理论，这项研究将继续发现，清楚地展示，并在未来几年和以后投入工作。

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.