Black Hole Perturbations and Gravitational Self Force Physics

该奖项支持的研究将对我们对广义相对论在极端天体物理系统中的应用的理解、对科学教育以及对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探测到引力波，都为研究宇宙打开了一扇新的窗口。这样的探测将允许我们对现有的引力理论进行新的测试，并将其应用到可以想象到的最极端的系统中。这些波的可能来源包括由黑洞、中子星和太阳质量的天体组成的双星系统，它们绕轨道运行并最终旋转成非常大的黑洞——质量是太阳的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。人们正在开发新的分析方法，以更有效地描述紧凑物体系统的时空动力学，例如旋转的黑洞双星，它们通过引力波的发射而进化。引力波探测的实验工作，以及最终对引力波源特性的分析，将直接受益于对引力波轨道的精确理论预测。为了继续这项工作，对引力自作用力效应的探索将继续进行。一旦从自力界获得二阶数值数据，将对数值和解析（后牛顿）结果进行新的比较。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会增加，对后牛顿膨胀本身的理解也会增加。新的规范不变量，具有二阶和高阶导数作用于度规，将系统地研究史瓦西和克尔黑洞的摄动，并寻求它们满足的方程。后一项工作将与南安普敦大学的一位同事以及与德国戈姆的阿尔伯特·爱因斯坦研究所有联系的几位数学同事合作进行。本文将仔细分析史瓦西几何和克尔几何问题之间的异同，以期使克尔时空背景下的自力计算更加有效。

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.