Abstract An outstanding prediction of general relativity is the fact that the angular momentum S of an isolated black hole with mass μ is limited by the Kerr bound, S ≤ G μ 2 / c . Testing this cornerstone is challenging due to the difficulty in modeling spinning compact objects that violate this bound. We argue that precise, model-independent tests can be achieved by measuring gravitational waves from an extreme mass ratio inspiral around a supermassive object, one of the main targets of the future LISA mission. In the extreme mass ratio limit, the dynamics of the small compact object depends only on its multipole moments, which are free parameters. At variance with the comparable-mass case, accurate waveforms are valid also when the spin of the small object greatly exceeds the Kerr bound. By computing the orbital dephasing and the gravitational-wave signal emitted by a spinning point particle in circular, nonprecessing, equatorial motion around a Kerr black hole, we estimate that LISA will be able to measure the spin of the small compact object at the level of 10%. Together with mass measurements, this will allow for theory-agnostic, unprecedented constraints on string-theory inspired objects such as “superspinars”, almost in their entire parameter space.

中文翻译：

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具有极端质量比螺旋的 Kerr 边界的模型独立测试

摘要 广义相对论的一个突出预测是质量为 μ 的孤立黑洞的角动量 S 受克尔界的限制，S ≤ G μ 2 / c 。由于难以对违反此界限的旋转紧凑物体进行建模，因此测试这一基石具有挑战性。我们认为，通过测量来自超大质量物体周围的极端质量比螺旋的引力波，可以实现精确的、独立于模型的测试，这是未来 LISA 任务的主要目标之一。在极端质量比限制下，小型紧凑物体的动力学仅取决于其多极矩，这是自由参数。与质量相当的情况不同，当小物体的自旋大大超过克尔界限时，准确的波形也是有效的。通过计算绕克尔黑洞进行圆形、非进动、赤道运动的自旋点粒子发出的轨道移相和引力波信号，我们估计 LISA 将能够在10%。与质量测量一起，这将允许对弦理论启发的对象（例如“超级旋流器”）几乎在其整个参数空间中的理论不可知、前所未有的约束。