We construct retarded and advanced Green’s functions for gravitational perturbations in Kerr in an ingoing radiation gauge. Our Green’s functions have a frequency domain piece that has previously been obtained by Ori (2003 Phys. Rev. D 67) based on the Chrzanowski-Cohen-Kegeles metric reconstruction method. As is well known, this piece by itself is not sufficient to obtain an actual Green’s function. We show how to complete it with a piece based on a method by Green et al (2020 Class. Quantum Grav. 37). The completion piece has a completely explicit form in the time-domain and is supported on pairs of points on the same outgoing principal null geodesic which are in the appropriate causal order. We expect our Green’s functions to be useful for gravitational self-force calculations and other perturbation problems on Kerr spacetime.

中文翻译：

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Spin-2 Green 对辐射计中 Kerr 的作用


我们在入射辐射计中构建了 Kerr 引力扰动的延迟和高级格林函数。我们的格林函数有一个频域部分，该频域部分之前已由 Ori （2003 Phys. Rev. D 67） 基于 Chrzanowski-Cohen-Kegeles 度量重建方法获得。众所周知，这块棋子本身不足以获得实际的格林函数。我们展示了如何用基于 Green 等人的方法（2020 Class. Quantum Grav.37）的文章来完成它。完成部分在时域中具有完全明确的形式，并且支持同一传出主零测地线上的点对，这些点以适当的因果顺序排列。我们期望格林函数对 Kerr 时空的引力自力计算和其他扰动问题有用。