Almost BPS black holes

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.