Axis potentials for stationary $n$-black-hole configurations

TL;DR

This paper generalizes the mathematical description of stationary multi-black-hole systems, providing a framework to analyze equilibrium configurations with multiple rotating and charged black holes using boundary data parametrization.

Contribution

It introduces the most general boundary data form for n-black-hole configurations, enabling focused future studies on these equilibrium solutions.

Findings

Derived the general boundary data for n-black-hole systems.

Provided a finite parameter set describing possible configurations.

Facilitated future analytical and numerical investigations of black-hole arrangements.

Abstract

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.