Black holes and fourfolds

26 pages, 1 figureInternational audienceWe establish the relation between the structure governing supersymmetric and non-supersymmetric four- and five-dimensional black holes and multicenter solutions and Calabi-Yau flux compactifications of M-theory and type IIB string theory. We find that the known BPS and almost-BPS multicenter black hole solutions can be interpreted as GKP compactifications with (2,1) and (0,3) imaginary self-dual flux. We also show that the most general GKP compactification leads to new classes of BPS and non-BPS multicenter solutions. We explore how these solutions fit into $N$=2 truncations, and elucidate how supersymmetry becomes camouflaged. As a necessary tool in our exploration we show how the fields in the largest $N$=2 truncation fit inside the six-torus compactification of eleven-dimensional supergravity