We construct analytical and regular solutions in four-dimensional General Relativity which represent multi-black hole systems immersed in external gravitational field configurations. The external field background is composed by an infinite multipolar expansion, which allows to regularise the conical singularities of an array of collinear static black holes. A stationary rotating generalisation is achieved by adding independent angular momenta and NUT parameters to each source of the binary configuration. Moreover, a charged extension of the binary black hole system at equilibrium is generated. Finally, we show that the binary Majumdar-Papapetrou solution is consistently recovered in the vanishing external field limit. All of these solutions reach an equilibrium state due to the external gravitational field only, avoiding in this way the presence of any string or strut defect.
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