Reduction without reduction: adding KK-monopoles to five-dimensional stationary axisymmetric solutions

We present a general method to add KK-monopole charge to any asymptotically flat stationary solution of five-dimensional general relativity with two commuting axial symmetries. The technique exploits the underlying SL(3, R) invariance of the system by identifying a particular element of the symmetry group which changes the asymptotic boundary condition and adds KK-monopole charge. Furthermore, we develop a set of technical tools which allow us to apply the SL(3, R) transformations to solutions produced by the inverse scattering method. As an example of our methods, we construct the exact solution describing a static black ring carrying KK-monopole charge.