Multi-black holes from nilpotent Lie algebra orbits

TL;DR

This paper characterizes multi-black hole solutions in supergravity theories using nilpotent Lie algebra orbits, revealing new non-BPS solutions and extending understanding beyond traditional BPS configurations.

Contribution

It introduces a Lie algebra orbit method to classify and derive both BPS and non-BPS multi-black hole solutions in supergravity, including explicit non-supersymmetric extremal cases.

Findings

Recovery of known BPS solutions with 32 harmonic functions

Discovery of non-BPS solutions with 29 harmonic functions

Explicit construction of non-supersymmetric extremal solutions

Abstract

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. For maximal supergravity, we not only recover the known BPS solutions depending on 32 independent harmonic functions, but in addition find a set of non-BPS solutions depending on 29 harmonic functions. While the BPS solutions can be understood within the appropriate N=2 truncation of N=8 supergravity, the general non-BPS solutions require the whole field content of the theory.