论文标题
潮汐变形和旋转黑洞的耗散
Tidal Deformation and Dissipation of Rotating Black Holes
论文作者
论文摘要
我们表明，当旋转黑洞被弱且绝热的引力场扰动时，它们不会经历任何潮汐变形。对象的潮汐可变形性通过所谓的“爱情数字”量化，该“爱情数字”描述了对象对其外部潮汐场的线性响应。在这项工作中，我们计算了Kerr黑洞的爱情数字，并发现它们消失了相同。我们还计算了黑洞的潮汐响应的耗散部分，由于事件范围的吸收性，这是没有变化的。我们的结果适用于黑洞自旋的任意值，对于电型和磁性扰动，以及潮汐场的多极膨胀中的所有顺序。我们的研究中纳入了事件范围和渐近无穷大的边界条件，因为它们对于理解这些潮汐效应的方式至关重要。在结束时，我们解决了一般相对论中的爱情数字的歧义问题，当考虑到这些边界条件时，我们认为这将解决。我们的发现为当前的努力提供了基本的投入，以通过二进制系统发出的重力波探测紧凑物体的性质。
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.
