Asymptotically locally Euclidean/Kaluza-Klein stationary vacuum black holes in five dimensions

We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in five dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean, in which spatial cross-sections at infinity have lens space L(p, q) topology, or asymptotically Kaluza-Klein so that spatial cross-sections at infinity are topologically S ¹ × S ² . These are nondegenerate black holes of cohomogeneity 2, with any number of horizon components, where the horizon cross-section topology is any one of the three admissible types: S ³ , S ¹ × S ² , or L(p, q). Uniqueness of these solutions is also established. Our method is to solve the relevant harmonic map problem with prescribed singularities, having target symmetric space SL(3, R)/SO(3). In addition, we analyze the possibility of conical singularities and find a large family for which geometric regularity is guaranteed.