Symmetry Orbits of Supergravity Black Holes - In Honor of Andrei Slavnov's 75th Birthday

TL;DR

This paper explores the classification of supergravity black hole solutions through their symmetry group orbits, emphasizing the role of nilpotent orbits and graded algebra decompositions in understanding extremal and BPS solutions.

Contribution

It introduces a framework for analyzing black hole solution families using duality symmetries, nilpotent orbits, and algebraic decompositions, advancing the understanding of their structure.

Findings

Black hole solutions form symmetry group orbits.

Extremal solutions are characterized by nilpotent orbits.

Graded algebra decompositions classify solution families.

Abstract

Black hole solutions of supergravity theories form families that realizing the deep nonlinear "duality" symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in the analysis of such solution families employs timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of extremal or BPS solutions are characterized by nilpotent orbits under the duality symmetries, based upon a tri-graded or penta-graded decomposition of the corresponding duality-group algebra.