Multi-centered rotating black holes in Kaluza-Klein theory

Abstract: The most general charged and rotating black hole in Kaluza-Klein theory is known to be described by the Rasheed-Larsen solution. When the under-rotating extremal limit of this solution is taken, it falls into a general class of solutions of Kaluza-Klein theory found by Cl\'ement, and is specified by two harmonic functions on a three-dimensional flat base space. We use this fact to generalise the single extremal black hole solution to one describing an arbitrary superposition of such black holes. These black holes carry non-zero electric and magnetic charges, which we set to be equal for simplicity, and are in general rotating with parallel or anti-parallel spin vectors. It is checked that the space-time outside the black holes is free of pathologies such as naked singularities and closed time-like curves.