Multi--black holes in Bertotti--Robinson spacetime

Abstract

We construct a new class of exact solutions describing multi-black holes in the Bertotti--Robinson spacetime, using the monodromy-matrix formalism associated with integrable sigma models. Starting from the extremal Reissner--Nordström black hole in the Bertotti--Robinson background, we derive the corresponding coset and monodromy matrices and show that they are governed by nilpotent algebraic structures. This property enables an explicit factorization of the monodromy matrix, allowing for a systematic reconstruction of the underlying gravitational solutions. We extend this construction to multi-center configurations by introducing multiple poles in the monodromy matrix, leading to Majumdar--Papapetrou--type solutions with Bertotti--Robinson asymptotics. Each center is shown to correspond to a regular extremal black hole with an $\mathrm{AdS}_2 \times S^2$ near-horizon geometry, and the asymptotic end likewise approaches a Bertotti--Robinson geometry. We further generalize the framework to stationary configurations in the Bertotti--Robinson spacetime, as well as to a broader class of Israel--Wilson--Perjés-type solutions, by considering more general nilpotent elements. Our results demonstrate that the monodromy-matrix approach provides a powerful and systematic framework for constructing multi-black hole solutions in nontrivial backgrounds, and suggest a promising route toward more general configurations.