Investigations in Gravitational Wave Sources and Numerical Relativity

将研究重力物理中的两个问题，每个问题对当前探测引力波和表征引力波源的努力都至关重要。首先，将使用基于牛顿/四极近似的三维计算机代码分析来自核心坍缩超新星的引力波。这项工作将决定动力不稳定性是否能成功地产生一个高度拉长或碎片化的内核，从而产生相应的大引力波信号。其次，“爱因斯坦-克里斯托费尔”广义相对论的双曲公式将被分析，特别强调发展一个稳定的，精确的数值算法。将在开发包含高分辨率冲击捕获方案的数值相对性代码方面取得进展。这样的代码将被用于研究引力冲击在天体物理系统中可能扮演的角色。此外，这些模拟是确定来自超新星的引力波是否可以被LIGO等接收器探测到的重要一步。

Two problems in gravitational physics will be studied, each of vitalimportance for the current efforts to detect gravitational waves andcharacterize gravitational wave sources. First, gravitational wavesfrom core-collapse supernovae will be analyzed using athree--dimensional computer code based on the Newtonian/quadrupoleapproximation. This work will determine whether dynamical instabilitiessucceed in producing a highly elongated or fragmented inner core, witha correspondingly large gravitational-wave signal. Second, the``Einstein--Christoffel" hyperbolic formulation of general relativitywill be analyzed with particular emphasis on developing a stable,accurate numerical algorithm. Progress will be made toward developing anumerical relativity code that encorporates a high-resolution shockcapturing scheme.Such codes will be needed to investigate the role that gravitationalshocks might play in astrophysical systems. Also, these simulationsconstitute an important step toward determining whether gravitationalwaves from supernovae can be detected by receivers such as LIGO.