We construct the first binary black hole solutions of Einstein-Maxwell theory in asymptotically anti-de Sitter space. The attractive force between the two black holes is balanced by the addition of a background electric field, sourced at the conformal boundary. There is a continuous family of bulk solutions for a given boundary profile and temperature, suggesting there is continuous non-uniqueness. We investigate the charges of the solutions and verify numerically that they satisfy a first law of black hole mechanics relation.
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BIGGS et al. (2024) studied this question.
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