Quantum Gravity and Relativistic Astrophysics

该项目包括两个部分：(1)天体物理研究的重点是产生近似引力波形的程序，以更快的时间尺度为正在进行的引力波探测实验提供有用的信息，而不是进行精确的数值模拟。在它们最后几个激发轨道，以及在它们最后的俯冲和合并中，这些双星强烈地弯曲时空，强烈地发出引力波。要完全理解这一过程，以及产生的引力波形，将需要进一步开发超级计算机进化代码。这里的方法是使用一个近似方案，用于渐变的后期双星，然后是超级计算机进化，用于最终的向内俯冲和空穴合并。该方法利用了渐变螺旋的时空与完全周期双星的时空差别很小的事实。因此，这个渐变的旋涡可以用一个精确的周期轨道来近似。这些周期轨道可以用来构造一个表示双星半径逐渐减小的准平衡序列，并很好地逼近相应的引力波形。(2)理论物理中的一个突出问题是如何使量子理论原理与广义相对论原理相协调。在广义相对论中，时空没有任何固定的结构，这种结构不是动态的，而是作为一个静止的动子从外部控制动力学。另一方面，量子理论依赖于这样的结构。这个项目将爱因斯坦的理论视为一个模型，人们可以在这个模型上阐明如何在不引入外部结构的情况下对没有外部结构的系统进行量子化。这里的第一个主要主题是，叶层不能被视为固定的元素，而是帮助我们从时空叶层建立相空间的自由变量。第二个主旋律更加具体。黑洞是由量子物质球体崩塌而形成的，它产生的量子几何没有其自身的自由度将被研究。将确定平均几何形状及其涨落，并研究在此背景下产生的辐射与热辐射场的不同之处。目前，相对论引力在天体物理的前沿和理论物理的前沿都引起了极大的兴趣。这个项目包含了这两种类型的研究。除了对引力物理学的两个前沿领域产生广泛影响外，该项目还将为博士后研究人员和学生提供广泛的理论培训。

This project contains two components: (1) The astrophysical research focuses on a program to produce approximate gravitational waveforms to provide useful information to ongoing gravitational wave detection experiments on a faster time scale than that likely to be needed for an accurate numerical simulation. In their last few orbits of inspiral, and in their final plungeand merger, these binaries strongly curve spacetime and strongly emit gravitational waves. A complete understanding of this process, and of the gravitational waveforms produced, will require much further development of supercomputer evolution codes. The approach here is to use an approximation scheme for the gradual late-stage binary inspiral followed by supercomputer evolution for the final inward plunge and merger of the holes. The method exploits the fact that the spacetime of the gradual inspiral differs very little from that of a perfectly periodic binary. This gradual inspiral is therefore approximated by an exactly periodic orbit. These periodic orbits can be used to construct a quasiequilibrium sequence representing the gradual pre-plunge decrease in radius of the binary, and to give a good approximation to the corresponding gravitational waveform. (2) An outstanding problem in theoretical physics is how to reconcile the principles of quantum theory with those of general relativity. In general relativity, spacetime does not have any fixed structure which is not dynamical but governs dynamics from outside as an unmoved mover. On the other hand, quantum theory depends on such structures. This project views Einstein's theory as a model on which one can clarify how to quantize a system with no external structure without introducing an external structure. The first main theme here is that foliations can be viewed not as fixed elements but as free variables which help us to build phase space from spacetime foliation. The second main theme is more specific. A black hole is formed by a spherical collapse of quantum matter that produces quantum geometry without its own degrees of freedom will be studied. A mean geometry and its fluctuations will be determined, and a study will be made of how the radiation produced on this background differs from the thermal radiation fields. At present, relativistic gravitation is of crucial interest both at the frontier of astrophysicsand at the frontier of theoretical physics. This project contains research of both types. In addition to its broad impacts on the two frontiers of gravitational physics, this project will also provide broad theoretical training to postdoctoral researchers and students.