Multi-Center non-BPS Black Holes - the Solution

We construct multi-center, non-supersymmetric four-dimensional solutions describing a rotating D6-D2 black hole and an arbitrary number of D4-D2-D0 black holes in a line. These solutions correspond to an arbitrary number of extremal non-BPS black rings in a TaubNUT space with a rotating three-charge black hole in the middle. The positions of the centers are determined by solving a set of “bubble” or “integrability” equations that contain cubic polynomials of the inter-center distance, and that allow scaling solutions even when the total four-dimensional angular momentum of the scaling centers is non-zero.