Numerical Simulation of Gravitational Wave Sources and Other Dynamical Spacetimes

该项目将开发必要的数学和计算技术，以便对引力辐射的实际天体物理源进行计算机模拟：特别是双黑洞和中子星星系统。 本研究将探讨以下技术问题：1）三维模拟双星黑洞问题的伪谱方法; 2）三维演化在不同形式的Einstein演化方程中的稳定性; 3）构造天体物理上真实的双星黑洞初始数据的各种方法; 4）动力学和规范演化方程的双曲形式; 5）单黑洞时空中标量场的尾效应; 6）求解Einstein演化方程的变分积分技术; 7）中子星星/黑洞双星中中子星的潮汐破裂; 8）轴对称时空的动力学; 9）具有自适应网格加密的全约束三维演化软件开发; 10）五维黑弦时空; 11）和特征自适应网格加密代码的开发。未来十年将是引力波（GW）科学令人兴奋的时刻。 在此期间，最初的LIGO（2002- 2006），其次是先进的LIGO（约。 2007- 2012年），然后是丽莎（CA。2011年）GW探测器应该可以运行。 这些探测器（LIGO在高频波段，10到2000 Hz，丽莎在低频波段，0.0001到0.1 Hz）将变得足够灵敏，以探测各种各样的天体物理GW源，如双黑洞和中子星星系统，它们对这些源的观测将使人们有可能做一个广泛的新科学。在某些情况下，GW搜索本身需要对这些源产生的波形进行理论预测，并且在所有情况下提取波的信息。 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。 最强和最有趣的来源将涉及具有强引力场的天体物理系统。 这些源是如此复杂和非线性，它们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，使其能够对现实的天体物理引力波源进行所需的模拟。

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.