It was shown recently that the static tidal response coefficients, called Love numbers, vanish identically for Kerr black holes in four dimensions. In this work, we confirm this result and extend it to the case of spin-0 and spin-1 perturbations. We compute the static response of Kerr black holes to scalar, electromagnetic, and gravitational fields at all orders in black hole spin. We use the unambiguous and gauge-invariant definition of Love numbers and their spin-0 and spin-1 analogs as Wilson coefficients of the point particle effective field theory. This definition also allows one to clearly distinguish between conservative and dissipative response contributions. We demonstrate that the behavior of Kerr black hole responses to spin-0 and spin-1 fields is very similar to that of the spin-2 perturbations. In particular, static conservative responses vanish identically for spinning black holes. This implies that vanishing Love numbers are a generic property of black holes in four-dimensional general relativity. We also show that the dissipative part of the response does not vanish even for static perturbations due to frame-dragging.

最近显示，静态潮汐响应系数，称为Love数，在四个维度上对Kerr黑洞的消失都相同。在这项工作中，我们确认了这个结果，并将其扩展到了spin-0和spin-1摄动的情况。我们计算黑洞自旋中所有阶数的Kerr黑洞对标量场，电磁场和引力场的静态响应。我们使用洛夫数及其自旋0和自旋1类似物的明确和规范不变的定义作为点粒子有效场论的威尔逊系数。这一定义还使人们可以清楚地区分保守反应和消散反应。我们证明了Kerr黑洞对spin-0和spin-1场的响应行为与spin-2扰动的行为非常相似。特别是，旋转黑洞时，静态保守响应会以相同的方式消失。这意味着消失的Love数是二维广义相对论中黑洞的一般属性。我们还表明，响应的耗散部分甚至不会因帧拖曳而产生的静态扰动消失。