Einstein's Equations as a Dynamical System

这项在数学和计算万有引力方面的研究，旨在使爱因斯坦的方程对我们在未来十年内对宇宙的观察更有用。约克教授将重点研究爱因斯坦演化方程的公式，这些公式在数学上是严谨的，对大规模数值实现和系统解析近似是有用的。在初值方程、正则作用原理和Bianchi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的方法，将其推广到爱因斯坦的理论中。我们还将研究存在理性的广义相对论统计热力学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，与那些已经、正在和将继续发生的实验和观测重力和宇宙学相匹配。在接下来的几年甚至更长时间里，这项研究将继续发现、清楚地展示并投入工作，这就是这样的理论。

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.