Octonionic black holes

Abstract

Using algebraic tools inspired by the study of nilpotent orbits in simple Lie algebras, we obtain a large class of solutions describing interacting non-BPS black holes in N = 8 supergravity, which depend on 44 harmonic functions. For this purpose, we consider a truncation E6(6)/Sp c(8,ℝ) ⊂ E8(8)/Spinc* (16) of the non-linear sigma model describing stationary solutions of the theory, which permits a reduction of algebraic computations to the multiplication of 27 by 27 matrices. The lift to N = 8 supergravity is then carried out without loss of information by using a pertinent representation of the moduli parametrizing E7(7)/SUc(8) in terms of complex valued Hermitian matrices over the split octonions, which generalise the projective coordinates of exceptional special Kähler manifolds. We extract the electromagnetic charges, mass and angular momenta of the solutions, and exhibit the duality invariance of the black holes distance separations. We discuss in particular a new type of interaction which appears when interacting non-BPS black holes are not aligned. Finally we will explain the possible generalisations toward the description of the most general stationary black hole solutions of N = 8 supergravity.