Black-Hole Dynamics and Gravitational Waves

我们将对数值相对论和引力波物理中的几个问题进行理论和数值研究。将开发一种数值方法来计算在黑洞附近传播的波场。这种方法将专注于直接计算时空度规，这是描述引力场的物体。与这项工作有关的是，将研究确定用于上述数值方法和用于更一般的数值相对论计算的最佳非反射边界条件。还将研究匹配过滤技术，该技术可用于分析来自LIGO探测器的数据，以搜索涉及两颗恒星显著自转(自转)水平的合并双星。发展一种计算黑洞背景下的时空度规的数值方法是重要的，原因有几个。这样的方法可能被用来计算围绕较大的旋转黑洞旋转的小黑洞的逐渐合并。像这样的合并在LIGO和拟议的NASA/ESA LISA任务中可能是可检测到的事件。黑洞背景波的计算也是检验数值计算稳定性的一个重要领域，这是目前数值相对论中一个相当普遍的问题。这种计算的非反射边界条件的规定因黑洞周围空间的曲率而变得复杂。发展更精确的无反射条件是准确计算引力波的重要组成部分，也可能是稳定某些数值计算的重要因素。现有的搜索LIGO数据的技术无法从一些合并的双星中检测到微弱的信号，这些双星具有显著的单独恒星自转速度。包括自旋效应很简单，但会导致计算上的困难。我们的目标将是找到一种搜索技术，在保持计算可行性的同时，结合SPIN的基本方面。

A theoretical and numerical study will be made of several problems in numerical relativity and gravitational wave physics. A numerical method will be developed to allow the calculation of wave fields that propagate in the vicinity of black holes. This method will focus on directly computing the spacetime metric, which is the object that describes a gravitational field. Related to this effort, a study will be made to determine optimal non-reflecting boundary conditions, for use in the above-mentioned numerical method and for use in more general numerical relativity calculations. A study will also be made of matched-filter techniques that can be applied in analyzing data from the LIGO detectors to search for merging binary stars which involvesignificant levels of spin (rotation) of the two stars.The development of a numerical method for computing the spacetime metric on a black hole background is important for several reasons. Such a method might be applied to calculate the gradual merger of a small black hole that is orbiting around a larger, rotating black hole. Mergers like this are potentially detectable events in LIGO and the proposed NASA/ESA LISA mission. Computation of waves on black hole backgrounds is also an important arena for testing the stability of numerical calculations, which is a considerable general concern in numerical relativity at present. Specification of non-reflective boundary conditions for such calculations is complicated by the curvature of space around black holes. Development of a more accurate non-reflecting condition is an important component to accurately computing gravitational waves and may be an important ingredient to stabilizing some numerical calculations. Existing techniques to search through LIGO data will not detect weak signals from some merging binaries which have significant individual stellar rotation rates. Including spin effects is straightforward but leads to a computationally prohibitive task. Thegoal will be to find a search technique that incorporates the essential aspects of spin while remaining computationally viable.