Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity

TL;DR

This paper classifies charge orbits and moduli spaces of extremal black holes in five-dimensional supergravity theories, providing a detailed mathematical framework for understanding their U-duality properties.

Contribution

It systematically derives the U-duality charge orbits and stabilizer groups for various classes of extremal black holes in 5D supergravity, including symmetric and non-symmetric scalar manifolds.

Findings

Classification of charge orbits for large and small black holes.

Explicit determination of stabilizer groups and moduli spaces.

Analysis of attractor solutions in different supergravity theories.

Abstract

We derive the U-duality charge orbits, as well as the related moduli spaces, of "large" and "small" extremal black holes in non-maximal ungauged Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5 space-time dimensions. The stabilizer groups of the various classes of orbits are obtained by determining and solving suitable U-invariant sets of constraints, both in "bare" and "dressed" charges bases, with various methods. After a general treatment of attractors in real special geometry (also considering non-symmetric cases), the N=2 "magic" theories, as well as the N=2 Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal (N=4) matter-coupled supergravity is also studied in this context.