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“聆听”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测试。 天文学家对超大质量黑洞（例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性。 然而，为了检验爱因斯坦的伟大理论，有必要了解它对实际测量的实际预测。 该项目延续了一项研究计划，旨在提供爱因斯坦理论的抽象美和复杂数学与物理学家和天文学家测量的现实世界之间的具体联系。 这些联系是通过以实用且可用的形式找到方程的近似但准确的解来建立的。 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利用新检测到的信号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此类物体运行的恒星。 爱因斯坦的理论是一个令公众着迷的话题，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，该项目将通过计算双星系统的运动方程以及发射的引力波形，增强地面引力波观测站（例如LIGO-Virgo网络）测试广义相对论的能力，正如一个重要的预测所预测的那样另一种理论，称为标量张量引力，在所谓的后牛顿近似中具有高精度。 它将以适合 LIGO-Virgo 数据分析方法的格式提供该理论预测的准确波形。 该方法扩展了 PI 及其合作者多年来开发的一种称为“松弛爱因斯坦方程直接积分”的方法。 PI 于 2008 年提出，将进一步研究使用未来红外望远镜在银河系中心大质量黑洞附近测试广义相对论的可能性。 将使用基于后牛顿近似的解析方法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。

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.