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

TL;DR

This paper classifies extremal black hole solutions in N=4 supergravity with n vector multiplets using nilpotent orbits of so(8,2+n), providing explicit non-BPS solutions with multiple harmonic functions.

Contribution

It introduces a novel classification framework for extremal black holes based on nilpotent orbits of so(8,2+n) and explicitly constructs new non-BPS solutions.

Findings

Derived general solutions from nilpotent orbit decompositions.

Explicitly constructed asymptotically Minkowski non-BPS solutions.

Demonstrated the formalism with solutions depending on 6+n harmonic functions.

Abstract

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 the most exotic class depending on 6+n harmonic functions.