Octonionic black holes

Understand

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(8,R) 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) / SU(8) in terms of complex valued Hermitian matrices over the split octonions, which generalise the projective coordinates of exceptional special Kaehler manifolds.
• We extract the electromagnetic charges, mass and angular momenta of the solutions, and exhibit the duality invariance of the black holes distance separations.