Relativistic Gravitation and Astrophysics

美国LIGO天文台最近探测到的引力波，展示了一种利用时空涟漪“听到”宇宙的新方法，并为爱因斯坦的广义相对论提供了令人惊叹的新检验。天文学家对超大质量黑洞（如银河系中心的黑洞）附近恒星和气体运动的观测，为在时空扭曲极端的领域检验爱因斯坦的理论提供了可能。然而，为了验证爱因斯坦的伟大理论，有必要知道它对实际测量的实际预测。这个项目继续了一项研究计划，旨在为爱因斯坦理论的抽象之美和复杂数学与物理学家和天文学家进行测量的现实世界之间提供具体联系。这些联系是通过找到近似的、精确的、实用的形式的方程解来建立的。在这项研究中开发的解决方案将被引力波天文台的数据专家用来使用新探测到的信号来更好地测试广义相对论，并将被天文学家用来探测大质量黑洞附近扭曲的时空如何影响围绕这些物体运行的恒星。爱因斯坦的理论是一个让公众着迷的话题，PI将继续就与这项研究相关的主题进行公开讲座，让更广泛的社区了解爱因斯坦的思想。具体来说，这个项目将有助于地面引力波观测站，如LIGO-Virgo网络，通过计算双星系统的运动方程，以及发射的重力波形，来测试广义相对论，正如一个重要的替代理论所预测的那样，被称为标量张量引力，在所谓的后牛顿近似中达到高精度。它将以一种可以适应LIGO-Virgo数据分析方法的格式提供由该理论预测的精确波形。该方法扩展了一种名为“放松爱因斯坦方程的直接积分”的方法，该方法已经由PI和他的合作者开发了多年。在银河系中心的大质量黑洞附近，使用PI在2008年提出的未来红外望远镜检验广义相对论的可能性将得到进一步的研究。广义相对论对大质量黑洞周围星团的结构和长期演化的影响将采用基于后牛顿近似的解析方法进行研究。

The recent detections of gravitational waves by the LIGO observatories in the USA have demonstrated a new way of "hearing" the universe using ripples in spacetime, and have provided stunning new tests of Einstein's theory of general relativity. Observations by astronomers of the motions of stars and gas near supermassive black holes, such as the one at the center of the Milky Way, have opened the possibility of testing Einstein's theory in realms where the warping of spacetime is extreme. Yet in order to test Einstein's great theory, it is essential to know what it actually predicts for real measurements. This project continues a program of research to provide concrete links between the abstract beauty and complex mathematics of Einstein's theory and the real world where measurements are made by physicists and astronomers. These links are established by finding approximate, yet accurate solutions of the equations in forms that are practical and usable. The solutions developed in this research will be used by data experts at the gravitational-wave observatories to perform better tests of general relativity using newly detected signals, and will be used by astronomers to probe how the warped spacetime near massive black holes affects stars orbiting such objects. Einstein's theory is a topic that fascinates the general public, and the PI will continue to give public lectures on topics related to this research, bringing understanding of Einstein's ideas to the broader community.Specifically, this project will contribute to the ability of ground-based gravitational-wave observatories such as the LIGO-Virgo network to test general relativity, by computing the equations of motion for binary star systems, along with the emitted gravitational waveforms, as predicted by an important alternative theory, known as scalar-tensor gravity, to high accuracy in the so-called post-Newtonian approximation. It will provide accurate waveforms predicted by this theory in a format that can be adapted to LIGO-Virgo data analysis methods. The approach extends a method known as Direct Integration of the Relaxed Einstein Equations that has been developed over many years by the PI and his collaborators. The possibility of testing general relativity in the vicinity of the massive black hole in the center of our galaxy using future infrared telescopes, proposed by the PI in 2008, will be investigated further. The effects of general relativity on the structure and long-term evolution of clusters of stars around massive black holes will be studied using analytic means based on the post-Newtonian approximation.