Interacting non-BPS black holes

TL;DR

This paper develops a systematic method using nilpotent orbits to find and classify extremal solutions in supergravity, revealing a new class of non-BPS multi-center black hole solutions with inverted brane orientations.

Contribution

It introduces a solvable linear system approach for extremal supergravity solutions and identifies a novel non-BPS class with interacting centers in the STU model.

Findings

Classified extremal solutions via nilpotent orbits: BPS, almost-BPS, and new non-BPS.

Explicit construction of a two-center non-BPS solution with inverted brane orientations.

Abstract

We explain how to exploit systematically the structure of nilpotent orbits to obtain a solvable system of equations describing extremal solutions of (super-)gravity theories, i.e. systems that can be solved in a linear way. We present the procedure in the case of the STU model, where we show that all extremal solutions with a flat three-dimensional base are fully described with the help of three different nilpotent orbits: the BPS, the almost-BPS and the composite non-BPS. The latter describes a new class of solutions for which the orientation of half of the constituent branes have been inverted with respect to the BPS one, such that all the centres are intrinsically non-BPS, and interact with each others. We finally recover explicitly the ensemble of the almost-BPS solutions in our formalism and present an explicit two-centre solution of the new class.