标题： 潮汐变形和旋转黑洞的耗散 显示英文标题

标题： Tidal Deformation and Dissipation of Rotating Black Holes

摘要： 我们证明，当旋转黑洞受到弱且绝热的引力场扰动时，不会经历任何潮汐形变。 物体的潮汐形变性由所谓的“洛夫数”来量化，这些数描述了物体对外部潮汐场的线性响应。 在本工作中，我们计算了克尔黑洞的洛夫数，并发现它们恒等于零。 我们还计算了黑洞潮汐响应的耗散部分，由于事件视界的吸收性质，该部分不为零。 我们的结果适用于任意自转速度的黑洞，无论是电型还是磁型扰动，并且适用于潮汐场多极展开的所有阶数。 事件视界和渐近无穷远的边界条件被纳入我们的研究中，因为它们对于理解这些潮汐效应如何映射到引力波观测量至关重要。 最后，我们讨论了广义相对论中洛夫数的模糊性问题，我们认为当考虑这些边界条件时，该问题得到解决。 我们的发现为当前通过双星系统发出的引力波探测致密天体性质的努力提供了关键输入。 显示英文摘要

摘要： We show that rotating black holes do not experience any tidal deformation when they are perturbed by a weak and adiabatic gravitational field. The tidal deformability of an object is quantified by the so-called "Love numbers", which describe the object's linear response to its external tidal field. In this work, we compute the Love numbers of Kerr black holes and find that they vanish identically. We also compute the dissipative part of the black hole's tidal response, which is non-vanishing due to the absorptive nature of the event horizon. Our results hold for arbitrary values of black hole spin, for both the electric-type and magnetic-type perturbations, and to all orders in the multipole expansion of the tidal field. The boundary conditions at the event horizon and at asymptotic infinity are incorporated in our study, as they are crucial for understanding the way in which these tidal effects are mapped onto gravitational-wave observables. In closing, we address the ambiguity issue of Love numbers in General Relativity, which we argue is resolved when those boundary conditions are taken into account. Our findings provide essential inputs for current efforts to probe the nature of compact objects through the gravitational waves emitted by binary systems.