Einstein's Equations as a Dynamical System

这项在数学和计算引力方面的研究旨在使爱因斯坦的方程对我们在未来十年内观测宇宙更有用。 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，对大规模数值计算和系统分析近似非常有用。 在初值方程、正则作用原理和比安奇恒等式方面也有了显著的改进。 这项工作将利用的方法，双曲型偏微分方程的数学文献，推广，以便适用于爱因斯坦的理论。 发展的某些基本概念所需的存在一个合理的广义相对论统计热力学也将进行研究。 在理解和实际应用引力理论方面存在着巨大的进步空间，与实验和观测引力和宇宙学的进步空间相匹配，这些进步空间已经、正在并将继续发生。 正是这样的理论，这项研究将继续发现，清楚地展示，并在未来几年及以后投入工作。

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.