Black Hole Perturbations and Gravitational Self Force Physics

该奖项支持的研究将对我们理解广义相对论在极端天体物理系统中的应用，科学教育以及公众对科学的理解和欣赏产生广泛影响。无论是在地球上还是在太空中，对引力波的探测都为我们打开了一扇了解宇宙的新窗口。这种探测将使我们当前的引力理论在应用于可以想象的最极端的系统时得到新的检验。这些波的可能来源包括黑洞和中子星的双星系统，以及围绕太阳质量轨道运行并最终螺旋进入非常大的黑洞-太阳质量的1000亿到100亿倍。这些来源包括宇宙中一些最令人惊讶的物体。正在开发新的分析方法，以更有效地描述致密物体系统的时空动力学，例如通过发射引力波而演化的旋转黑洞双星。引力波探测的实验工作以及最终的源特性分析将直接受益于轨道轨迹的精确理论预测。为了进行这项工作，将继续探索引力自力效应。一个新的数值和分析（后牛顿）的结果之间的比较将二阶数值数据成为可从自力社区。这项工作是与巴黎天体物理研究所的同事和佛罗里达大学的博士后合作进行的。对自作用力和后牛顿计算所需的正则化的信心将增加，对后牛顿膨胀本身的理解也将增加。新的规范不变量，与二阶和高阶导数作用于度量，将系统地调查的史瓦西和克尔黑洞的扰动，并将寻求他们满足的方程。后一项工作将与南安普顿大学的一位同事以及与德国戈尔姆的阿尔伯特爱因斯坦研究所有联系的几位数学同事合作进行。在史瓦西和克尔几何的问题之间的相似性和差异将仔细分析，以期使自力计算在克尔时空背景更有效。

This award supports research that will have a broad impact upon our understanding of the applications of General Relativity to extreme astrophysical systems, upon science education, and upon understanding and appreciation of science by the public. The detection of gravitational waves, either on Earth or in space, is opening a new window on the universe. Such detections will allow new tests of our current theory of gravity when applied to the most extreme systems imaginable. Likely sources of these waves include binary systems of black holes and neutron stars and solar mass objects orbiting and eventually spiraling into very large black holes - one thousand to ten billion times the mass of the Sun. These sources include some of the most surprising objects in the universe. New analysis is being developed to more efficiently describe the spacetime dynamics of systems of compact objects, such as rotating black hole binaries, which evolve through the emission of gravitational waves. The experimental effort leading toward the detection of gravitational waves and, ultimately, the analysis of the source characteristics will directly benefit from accurate theoretical prediction of the orbital trajectories.To pursue this work, the exploration of gravitational self force effects will continue. A new comparison between numerical and analytical (post-Newtonian) results will be made once second order numerical data becomes available from the self force community. This work is carried out in collaboration with colleagues at the Institute of Astrophysics in Paris and with a postdoc at UF. Confidence in the regularization required for both self force and post-Newtonian calculations will be increased, as will understanding of the post-Newtonian expansion itself. New gauge invariant quantities, with second and higher order derivatives acting on the metric, will be systematically investigated for perturbations of the Schwarzschild and Kerr black holes, and equations which they satisfy will be sought. This latter effort will be carried out in collaboration with a colleague in Southampton University, and with several mathematical colleagues with ties to the Albert Einstein Institute in Golm, Germany. The similarities and differences between problems in the Schwarzschild and Kerr geometries will be carefully analyzed with a view to making self force calculations in the Kerr spacetime background more efficient.