发表机构
University of Southampton; University of Nottingham; University College Dublin; The University of Texas at Austin（南安普顿大学; 诺丁汉大学; 都柏林大学学院; 德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于二阶Teukolsky方程的新方案计算非旋转准圆双星系统的引力自力，可推广至Kerr背景，并消除红外发散，验证能量通量。
AI 中文摘要
目前，唯一的二阶引力自力计算是基于在Lorenz规范下直接求解微扰爱因斯坦方程。该方法依赖于爱因斯坦方程在Schwarzschild背景下的完全可分离性。在本文中，我们提出了一种基于二阶Teukolsky方程的新方案。关键在于，该方法有望（相当直接地）推广到更现实的Kerr背景情形。这里我们在围绕Schwarzschild黑洞的准圆轨道这一最简单设定中实施该方案。除了使用Teukolsky方程外，我们的方案还融合了相对于以往二阶自力计算的若干其他进展：紧致化双曲切片、变换到Bondi-Sachs规范，以及谱方法与参数变易法的结合。我们还利用这些工具重新审视了二阶Lorenz规范计算中出现的红外发散，表明它们在Teukolsky情形下不那么显著，并在Bondi-Sachs规范中被完全消除。最后，我们计算了渐近能量通量，并将其与以往的Lorenz规范计算结果进行了基准比较。
英文摘要
Currently, the only second-order gravitational self-force calculations have been based on directly solving the perturbative Einstein equations in the Lorenz gauge. That method relied on the complete separability of the Einstein equations in a Schwarzschild background. In this paper, we present a new scheme based on the second-order Teukolsky equation. Crucially, this method promises to extend (reasonably straightforwardly) to the more realistic case of a Kerr background. Here we implement the scheme in the simplest setting of quasicircular orbits around a Schwarzschild black hole. In addition to working with the Teukolsky equation, our scheme incorporates several other advances over previous second-order self-force calculations: compactified hyperboloidal slicing, transformation to a Bondi-Sachs gauge, and a combination of spectral and variation-of-parameters methods. We also use these tools to re-examine the infrared divergences that arise in second-order Lorenz-gauge calculations, showing they are less pronounced in the Teukolsky case and completely eliminated in the Bondi-Sachs gauge. We conclude by calculating the asymptotic energy fluxes and benchmarking them against previous Lorenz-gauge calculations.
Comments43 pages, 7 figures
