Relativistic Gravitation and Astrophysics

从天体物理源探测到引力波的可能性将为天文学打开一扇新的窗口，并为爱因斯坦的广义相对论提供新的检验。解释观测结果和推进这一新领域将需要对来自给定源的波信号进行准确的理论预测。该项目将使用由PI和他在华盛顿大学的学生开发的一种名为“放松爱因斯坦方程的直接积分”（DIRE）的方法，该方法系统地解决了爱因斯坦方程，该过程被称为后牛顿近似（适用于速度与光速相比较小的系统）。使用这种方法，将有可能以很高的精度研究致密双星系统（包含中子星或黑洞的双星系统）的吸入的详细运动和辐射。后牛顿方法还将用于研究围绕旋转黑洞的弯曲时空的不同寻常的方面，这些方面与所谓的“卡特”运动常数的存在有关，并计算由紧密双星合并形成的黑洞所经历的反冲力速度。此外，还将研究如何利用引力波数据来测试新体制下的其他引力理论，以及测量天体物理学和宇宙学参数。特别地，在广义相对论的一类“标量张量”替代方案中，将对紧致双星启发的引力辐射进行详细分析，同时研究数据分析策略，以便在这类理论上放置尽可能好的边界。利用未来的自适应光学红外干涉测量技术在银河系中心大质量黑洞强场附近测试广义相对论的可能性，将通过研究中心区域其他恒星对黑洞附近近轨恒星的轨道扰动、暗物质的可能分布以及恒星的潮汐畸变来分析。这将包括分析后牛顿计算和数值N体模拟的混合。在运动方程、引力波波形和引力波数据分析方面的工作将影响到新兴的引力波天文学领域。对反冲速度的研究可能会对天体物理模型中星系中大质量黑洞的形成以及后牛顿理论和数值相对论之间的联系产生重要影响。在银河系中心黑洞附近测试广义相对论的工作可能会影响红外天文观测先进仪器的发展。学生的教育和培训将被纳入研究计划。

The likely detection of gravitational waves from astrophysical sources will open a new window for astronomy and provide new tests of Einstein's theory of general relativity. Interpreting the observations and advancing this new field will require accurate theoretical predictions for the wave signal from a given source. This project will make use of a method known as Direct Integration of the Relaxed Einstein Equations (DIRE), that has been developed by the PI and his students at Washington University, which solves Einstein's equations systematically in a procedure known as the post-Newtonian approximation (appropriate for systems where the velocities are small compared to the speed of light). Using this method, it will be possible to study the detailed motion and radiation from the inspiral of compact binary systems (double star systems containing neutron stars or black holes) to a high degree of accuracy. Post-Newtonian methods will also be used to study unusual aspects of the curved spacetime surrounding rotating black holes, related to the existence of the so-called "Carter" constant of the motion, and to calculate the recoil velocity experienced by black holes formed from compact binary merger. Ways to use gravitational-wave data to test alternative theories of gravity in new regimes and to measure astrophysical and cosmological parameters will also be studied. In particular, a detailed analysis of gravitational radiation from compact binary inspiral in a class of "scalar-tensor" alternatives to general relativity will be carried out, together with a study of data analysis strategies for placing the best possible bound on this class of theories. The possibility of testing general relativity in the strong-field vicinity of the massive black hole in the center of our galaxy using future adaptive optics infrared interferometry will be analyzed by studying orbital perturbations of stars in close orbits near the hole caused by other stars in the central region, by a possible distribution of dark matter, and by tidal distortions of the stars. This will involve a mixture of analytical post-Newtonian calculations and numerical N- body simulations.The work on equations of motion, gravitational waveforms and analysis of gravitational-wave data will impact the emerging field of gravitational-wave astronomy. The work on recoil velocities may contribute important insights that could impact astrophysical modeling of the growth of massive black holes in galaxies, as well as the interface between post-Newtonian theory and numerical relativity. The work on testing general relativity near the galactic center black hole could impact the development of advanced instrumentation for observational infrared astronomy. Education and training of students will be integrated into the research program.