Charged and rotating multi-black holes in an external gravitational field

TL;DR

This paper constructs analytical solutions for multi-black hole systems in four-dimensional General Relativity immersed in external gravitational fields, including rotation and charge, avoiding conical singularities and string defects.

Contribution

It introduces a method to regularize multi-black hole configurations with external fields, incorporating rotation, charge, and NUT parameters, and recovers known solutions in specific limits.

Findings

Regular multi-black hole solutions in external fields are constructed.

Solutions include rotating, charged, and NUT parameter extensions.

The binary Majumdar-Papapetrou solution is recovered in the zero external field limit.

Abstract

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.