Non-BPS Black Rings and Black Holes in Taub-NUT

TL;DR

This work develops explicit non-BPS extremal multi-center solutions in Taub-NUT by employing the almost BPS framework, revealing non-BPS three-charge black rings and a rotating five-charge black hole as a seed for the most general under-rotating non-BPS 4D black hole in the STU model. The authors provide a detailed construction based on a Gibbons-Hawking base, solve the linear system for warp factors and the angular-momentum one-form, and analyze regularity, near-horizon geometry, and four-dimensional charges. A key result is that the non-BPS ring shares the near-horizon structure and entropy with its BPS counterpart, while its global ring radius is fixed by non-BPS bubble-like constraints, leading to a cubic generalization of the bubble equations. They also show that a non-BPS two-center system consisting of a ring and a black hole exists, with a horizon geometry and charges that generalize known BPS bound states, and demonstrate that their rotating non-BPS black hole solution lies in the duality orbit of under-rotating Rasheed-Larsen black holes. Overall, the paper bridges the gap between fake-superpotential approaches and Taub-NUT embeddings, offering seeds for broader families of non-BPS microstate geometries and multi-center configurations.

Abstract

We solve the recently-proposed equations describing non-BPS extremal multi-center configurations, and construct explicit solutions describing non-supersymmetric extremal black rings in Taub-NUT, as well as the seed solution for the most general extremal non-BPS under-rotating black hole in four dimensions. We also find solutions that contain both a black hole and a black ring, which descend to four-dimensional extremal non-BPS two-center black holes with generic charges.