标题： 在克尔时空中的任意束缚测地线上的引力自力 显示英文标题

标题： Gravitational self-force on generic bound geodesics in Kerr spacetime

摘要： 在本工作中，我们首次计算了质量比的一阶条件下克尔时空中一般束缚测地线的引力自力。也就是说，由于其对引力场自身的影响，导致绕较大旋转黑洞运行的致密天体运动方程的局部修正。这包括耗散效应和保守效应。我们的方法建立并扩展了先前用于计算赤道轨道上引力自力的方法。特别是，我们从威因斯坦标量$\psi_4$重建了向外辐射规范下的局部度规扰动，而该标量则是通过使用半解析频域方法求解泰科斯基方程得到的。随后，使用（球面）$l$模正则化获得引力自力。我们通过将大$l$行为与已知的解析正则化参数进行比较来测试我们的实现。此外，我们通过将能量、角动量和卡特常数的长期平均变化与从引力波通量到无限远和下至视界推导出的这些守恒量的变化进行比较来验证我们的结果。 显示英文摘要

摘要： In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass-ratio. That is, the local correction to equations of motion for a compact object orbiting a larger rotating black hole due to its own impact on the gravitational field. This includes both dissipative and conservative effects. Our method builds on and extends earlier methods for calculating the gravitational self-force on equatorial orbits. In particular we reconstruct the local metric perturbation in the outgoing radiation gauge from the Weyl scalar $\psi_4$, which in turn is obtained by solving the Teukolsky equation using semi-analytical frequency domain methods. The gravitational self-force is subsequently obtained using (spherical) $l$-mode regularization. We test our implementation by comparing the large $l$-behaviour against the analytically known regularization parameters. In addition we validate our results be comparing the long-term average changes to the energy, angular momentum, and Carter constant to changes to these constants of motion inferred from the gravitational wave flux to infinity and down the horizon.