We extend earlier discussions of the balance problem for two black holes and study stationary spacetimes containing an arbitrary number of $n$ aligned rotating and (possibly) charged black holes. For these hypothetical equilibrium configurations, we obtain the most general form of the boundary data on the symmetry axis in terms of a finite number of parameters. Hence future investigations of $n$-black-hole configurations can be restricted to studying properties of these finite families of solutions.

中文翻译：

---

固定 n 黑洞配置的轴势

我们扩展了先前对两个黑洞平衡问题的讨论，并研究了包含任意数量的 $n$ 对齐旋转和（可能）带电黑洞的静止时空。对于这些假设的平衡配置，我们根据有限数量的参数获得对称轴上边界数据的最一般形式。因此，未来对 $n$-黑洞配置的研究可能仅限于研究这些有限解系列的性质。