Multi-Center non-BPS Black Holes - the Solution

TL;DR

The paper extends the BPS multi-center framework to non-BPS black holes by building almost-BPS solutions on a Taub-NUT base that describe a rotating central D6-bar-D2 black hole with an arbitrary number of concentric D4-D2-D0 rings. It derives a complete set of warp factors, field strengths, and a detailed angular momentum structure, with center positions constrained by nonlinear bubble equations that are cubic in inter-center distances, yet admit scaling regimes. Regularity requires eliminating Dirac-Misner strings and ensuring horizon regularity, yielding horizon areas tied to the charges and a quartic invariant, while scaling limits reproduce a BPS-like structure even with nonzero 4D angular momentum. The results pave the way for non-BPS microstate geometries and motivate future work on tilted ring configurations, quiver interpretations, marginal stability lines, and duality-based routes to smooth non-BPS microstates.

Abstract

We construct multi-center, non-supersymmetric four-dimensional solutions describing a rotating anti-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 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.