N-black hole stationary and axially symmetric solutions of the Einstein/Maxwell equations

The Einstein/Maxwell equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ: ℝ³ \ Σ → ℍ²_ℂ, where Σ is a subset of the axis of symmetry, and ℍ²_ℂ is the complex hyperbolic plane. Motivated by this problem, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ: ℝⁿ \ Σ → ℍ, where Σ is a submanifold of ℝⁿ of co-dimension ≥ 2, and ℍ is a classical Riemannian globally symmetric space of noncompact type and rank one. This result, when applied to the black hole problem, yields solutions which can be interpreted as equilibrium configurations of multiple co-axially rotating charged black holes held apart by singular struts.