Non-supersymmetric microstates of the D1-D5-KK system

We construct a discrete family of smooth non-supersymmetric three charge geometries carrying D1 brane, D5 brane and Kaluza-Klein monopole charges in Type 1113 supergravity compactified on a six-torus, which can be interpreted as the geometric description of some special states of the brane system. These solutions are asymptotically flat in four dimensions, and generalise previous supersymmetric solutions. The solutions have a qualitatively similar structure to previous non-supersymmetric smooth solutions carrying D1 and D5 brane charges in five dimensions, and indeed can be viewed as the five-dimensional system placed at the core of a Kaluza-Klein monopole. The geometries are smooth, free of horizons and do not have closed timelike curves. One notable difference from the five-dimensional case is that the four-dimensional geometry has no ergoregion.