Quantum Gravity and Relativistic Astrophysics

该计划的相对论天体物理学部分由密切相关的项目组成，结合了数值和分析方法，所有这些都是为了理解黑洞碰撞。这项工作的动机来自三个方面。首先，黑洞碰撞是相对论引力中典型的非线性现象。其次，黑洞碰撞是最可能（当然也是最令人兴奋的）引力波来源之一，即将到来的引力波观测站将探测到它。第三，黑洞碰撞是在超级计算机上发展数值相对论的试验场。这项工作通过提供结果测试、指出有趣的计算案例以及提出可能在计算方法中有用的近似方案来支持这一发展。另一组正在研究的问题旨在理解爱因斯坦理论的规范量子化。黑洞再次成为人们关注的焦点，现在是在亚微观尺度上。具体项目包括研究量子引力对裸奇点和覆盖奇点形成的影响，黑洞内的质量膨胀，以及零静质量场可以用零尘描述的高频极限中的视界形成。另一个主要研究领域更为基本和普遍；它的目标是澄清微分同构不变性、约束和可观察对象之间的联系。具体项目包括正则变换的时空微分同态表示和正则重力中kretschmann型可观测值的研究

***9734871PriceThe relativistic astrophysics portion of the program consists of closely related projects, combining numerical and analytic approaches, all directed towards understanding black hole collisions. The motivation of this work comes from three directions. First, black hole collisions are an example of quintessentially nonlinear phenomena in relativistic gravitation. Second, black hole collisions are one of the most likely (and certainly the most exciting) sources of gravitational waves that will be detectable with forthcoming gravitational wave observatories. Third, black hole collisions are a testing ground for the development of numerical relativity on supercomputers. This work supports that development by providing tests of results, by pointing to interesting cases for computation, and by suggesting approximation schemes that may be useful in a computational approach.Another set of problems under study aims at understanding the canonical quantization of Einstein's theory. Black holes are again at the center of attention, now at the submicroscopic scale. Specific projects include studying the effects of quantum gravity on formation of naked and covered singularities, mass inflation inside black holes, and horizon formation in the high-frequency limit in which zero-rest-mass fields can be described by null dust. Another main area of research is more fundamental and general; its goal is to clarify the connection among diffeomorphism invariance, constraints and observables. Specific projects include the representation of spacetime diffeomorphisms by canonical transformations and the study of Kretschmann-type observables in canonical gravity.***