Quantum Gravity and Relativistic Astrophysics

* 9734871 Price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。 这项工作的动力来自三个方向。 首先，黑洞碰撞是相对论引力中典型的非线性现象。 其次，黑洞碰撞是最有可能（当然也是最令人兴奋的）的引力波源之一，即将到来的引力波观测站将可以探测到。 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。 这项工作支持的发展，提供测试的结果，通过指出有趣的情况下计算，并建议近似计划，可能是有用的计算approaches.Another一组正在研究的问题，旨在了解爱因斯坦理论的正则量子化。 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，黑洞内部的质量膨胀，以及零静止质量场可以用零尘埃描述的高频极限中的视界形成。 另一个主要的研究领域是更基本和一般的;其目标是澄清同胚不变性，约束和可观测量之间的联系。 具体的项目包括时空的正则变换和正则引力中的Kretschmann型观测量的研究表示。

***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.***