Almost BPS black holes

TL;DR

The paper develops a systematic method to generate non-BPS extremal black holes in four-dimensional N=2 supergravity by uplifting to five dimensions where a large class of 'almost BPS' solutions exist. These solutions are locally supersymmetric on patches (constructed by patching BPS flat-base data over a general Gibbons-Hawking base) and obey a first-order flow governed by harmonic functions, with a precise 4D/5D dictionary obtained via circle reduction. The authors provide explicit examples, including a non-BPS single-centre electric black hole and a two-centre non-BPS ring configuration, showing that the four-dimensional mass is a simple sum of charges (marginal states) and that the near-horizon attractor structure mirrors the BPS case. The work clarifies why certain non-BPS features are hidden in the full non-BPS spectrum while offering seed solutions to generate further cases through dualities, and it discusses potential extensions to symplectic formulations and higher-derivative corrections.

Abstract

We study non-BPS black hole solutions to ungauged supergravity with 8 supercharges coupled to vector multiplets in four and five dimensions. We identify a large class of five dimensional non-BPS solutions, which we call "almost BPS", that are supersymmetric on local patches and satisfy a first order flow governed by harmonic functions. By dimensional reduction, they give rise to new non-BPS solutions in four dimensions. These solutions allow for some nontrivial asymptotic moduli and multiple centres, similar to their globally supersymmetric cousins. We explicitly discuss a single centre and a two centre example.