THE GEOMETRY AND TOPOLOGY OF STATIONARY MULTIAXISYMMETRIC VACUUM BLACK HOLES IN HIGHER DIMENSIONS

Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in (n+3)-dimensional spacetimes admitting the isometry group R×U(1)ⁿ, with Kaluza–Klein asymptotics for n ≥ 3. This is equivalent to establishing existence and uniqueness for singular harmonic maps φ: R³ \ Γ → SL(n + 1,R)/SO(n + 1) with prescribed blow-up along Γ, a subset of the z-axis in R³. We also analyze the topology of the domain of outer communication for these spacetimes, by developing an appropriate generalization of the plumbing construction used in the lower-dimensional case. Furthermore, we provide a counterexample to a conjecture of Hollands–Ishibashi concerning the topological classification of the domain of outer communication.