Numerical Simulation of Gravitational Wave Sources and Other Dynamical Spacetimes

引力波源和其他动态时空的数值模拟

• 批准号: 0244906
• 负责人: Lee Lindblom
• 金额: $ 24万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0244906&HistoricalAwards=false
• 关键词: Numerical; Simulation; Gravitational; Wave; Sources

This project will develop mathematical and computational techniques needed to perform computer simulations of realistic astrophysical sources of gravitational radiation: in particular binary black hole and neutron star systems. This research will investigate the following technical problems: 1) pseudo-spectral methods for use in 3D simulations of the binary black hole problem; 2) stability of 3D evolutions in various formulations of the Einstein evolution equations; 3) various methods of constructing astrophysically realistic binary black hole initial data; 4) hyperbolic formulationsof the combined dynamical and gauge evolution equations; 5) tail effects in scalar fields in single black hole spacetimes; 6)variational integration techniques for solving the Einstein evolutionequations; 7) tidal disruption of neutron stars in neutron star/black hole binaries; 8) the dynamics of axisymmetric spacetimes; 9) software development for fully constrained 3D evolution with adaptive mesh refinement; 10) 5D black string spacetimes; 11) and characteristic adaptive mesh refinement code development.The next decade will be an exciting time for gravitational wave (GW) science. During this time the initial LIGO (2002--2006), followed by the advanced LIGO (ca. 2007--2012), and then the LISA (ca. 2011) GW detectors should become operational. These detectors (LIGO in the high-frequency band, 10 to 2000 Hz, and LISA in the low-frequency band, 0.0001 to 0.1 Hz) will become sensitive enough to detect a wide variety of astrophysical GW sources such as binary black hole and neutron star systems, and their observations of these sources will make it possible to do a wide range of new science. Theoretical predictions of the waveforms generated by these sources will be needed for GW searches themselves in some cases, and for extracting the waves' information in all cases. Only by comparing theoretical waveforms with observed ones will it be possible to deducethe nature, structure and dynamics of the source. The strongest and most interesting sources will involve astrophysical systems with strong gravitational fields. These sources are so complex andnonlinear that they can be analyzed only with fully dynamical numerical simulations. This project will develop the mathematical and computational tools that will make it possible to perform the needed simulations of realistic astrophysical gravitational wave sources.

该项目将开发对引力辐射的真实天体物理来源进行计算机模拟所需的数学和计算技术：特别是双星黑洞和中子星系统。这项研究将研究以下技术问题：1)用于双星黑洞问题三维模拟的伪谱方法；2)爱因斯坦演化方程各种形式的3D演化的稳定性；3)构造天体物理上真实的双核黑洞初始数据的各种方法；4)组合动力学和规范演化方程的双曲公式；5)单个黑洞时空中标量场的尾部效应；6)求解爱因斯坦演化方程的变分积分技术；7)中子星/黑洞双星中的潮汐分裂；8)轴对称时空的动力学；9)自适应网格细化的完全约束三维演化的软件开发；10)5维黑弦时空；11)和特征自适应网格精化代码的开发。下一个十年将是引力波(GW)科学令人兴奋的时期。在此期间，最初的LIGO(2002-2006年)、紧随其后的高级LIGO(约2007-2012)以及LISA(约2011)GW探测器应投入使用。这些探测器(高频波段的LIGO和低频波段的LISA，频率为0.0001到0.1HZ)将变得足够灵敏，可以探测到各种天体物理GW源，如双星黑洞和中子星系统，它们对这些源的观测将使开展广泛的新科学成为可能。在某些情况下，GW搜索本身以及在所有情况下提取波的信息都需要对这些源产生的波形进行理论预测。只有将理论波形与观测波形进行比较，才有可能推断出震源的性质、结构和动力学。最强烈和最有趣的来源将涉及具有强大引力场的天体物理系统。这些源是如此复杂和非线性，以至于只能用完全动态的数值模拟来分析。该项目将开发数学和计算工具，使其有可能对现实天体物理引力波源进行所需的模拟。