Multi-black holes from nilpotent Lie algebra orbits

Understand

For N \ge 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 dimensions.
• As the main result of this paper, we show that whenever this pseudo-Riemanniann space is an irreducible symmetric space G/H*, the most general solutions of this type can be entirely characterised and derived from the nilpotent orbits of the associated Lie algebra Lie(G).
• This technique also permits the explicit computation of non-supersymmetric extremal solutions which cannot be obtained by truncation to N=2 supergravity theories.