Multi-center non-BPS black holes - the solution

We construct multi-center, non-supersymmetric four-dimensional solutions describing a rotating (D6) over bar -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 Taub-NUT 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.