For any number n of aligned black holes the axis potentials are necessarily rational functions depending on a finite number of parameters.
and Cederbaum, C.,A universal inequality between the angular momen- tum and horizon area for axisymmetric and stationary black holes with surrounding matter, Class
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The balance problem for $n$ aligned black holes
For any number n of aligned black holes the axis potentials are necessarily rational functions depending on a finite number of parameters.