Multi-black holes from nilpotent Lie algebra orbits

Multi-black holes from nilpotent Lie algebra orbits

For N ≥ 2 supergravities, BPS black hole solutions preserving four supersymmetries can be superposed linearly, leading to well defined solutions containing an arbitrary number of such BPS black holes at arbitrary positions. Being stationary, these solutions can be understood via associated non-linear sigma models over pseudo-Riemaniann spaces coupled to Euclidean gravity in three spatial dimens...

Extremal black holes and nilpotent orbits

The stationary solutions of a large variety of (super)gravity theories can be described within a non-linear sigma model G/H∗ coupled to Euclidean gravity in three-dimensions, for which G is a simple group and H∗ a non-compact real form of its maximal compact subgroup. The absence of naked singularities in four dimensions requires the G Noether charge in 3D to satisfy a characteristic equation t...

Extremal black holes, nilpotent orbits and the true fake superpotential

Dimensional reduction along time offers a powerful way to study stationary solutions of 4D symmetric supergravity models via group-theoretical methods. We apply this approach systematically to extremal, BPS and non-BPS, spherically symmetric black holes, and obtain their “fake superpotential” W . The latter provides first order equations for the radial problem, governs the mass and entropy form...

The extremal black holes of N = 4 supergravity from so ( 8 , 2 + n ) nilpotent orbits

We consider the stationary solutions of N = 4 supergravity coupled to n vector multiplets that define linear superpositions of non-interacting extremal black holes. The most general solutions of this type are derived from the graded decompositions of so(8, 2 + n) associated to its nilpotent orbits. We illustrate the formalism by giving explicitly asymptotically Minkowski non-BPS solutions of th...

Equivariant D-modules Attached to Nilpotent Orbits in a Semisimple Lie Algebra