We propose a new approach to find magnetically-dominated force-free (FF) magnetospheres around highly spinning black holes, relevant for models of astrophysical jets. Employing the near-horizon extreme Kerr (NHEK) limit of the Kerr black hole, any stationary, axisymmetric and regular FF magnetosphere reduces to the same attractor solution in the NHEK limit with null electromagnetic field strength. We use this attractor solution as the universal starting point for perturbing away from the NHEK region in the extreme Kerr spacetime. We demonstrate that by going to second order in perturbation theory, it is possible to find magnetically dominated magnetospheres around the extreme Kerr black hole. Furthermore, we consider the near-horizon near-extreme Kerr (near-NHEK) limit that provides access to a different regime of highly spinning black holes. Also in this case we find a novel FF attractor, which can be used as the universal starting point for a perturbative construction of FF magnetospheres. Finally, we discuss the relation between the NHEK and near-NHEK attractors.

我们提出了一种新方法，可以在高度旋转的黑洞周围寻找磁主导的无力 (FF) 磁层，这与天体物理喷流模型相关。利用克尔黑洞的近地平线极端克尔 (NHEK) 极限，任何静止的、轴对称的和规则的 FF 磁层都减少到具有零电磁场强度的 NHEK 极限中的相同吸引子解。我们使用这个吸引子解决方案作为在极端克尔时空中扰动远离 NHEK 区域的通用起点。我们证明，通过进入扰动理论的二阶，可以在极端克尔黑洞周围找到以磁为主的磁层。此外，我们考虑了近地平线近极端克尔（near-NHEK）极限，它提供了进入高度旋转黑洞的不同状态的途径。同样在这种情况下，我们发现了一个新的 FF 吸引子，它可以用作 FF 磁层微扰构造的通用起点。最后，我们讨论了 NHEK 和近 NHEK 吸引子之间的关系。