Extremal limits of the Cvetic-Youm black hole and nilpotent orbits of G2(2)

TL;DR

This paper explores the extremal limits of five-dimensional black holes in supergravity using nilpotent orbits of the Lie algebra G2(2), revealing a correspondence between orbit structure and black hole phase diagrams.

Contribution

It establishes a novel connection between nilpotent orbits of G2(2) and the classification of extremal black holes in supergravity, including both supersymmetric and non-supersymmetric cases.

Findings

Both black hole branches are characterized by nilpotent SO(2,2)-orbits.

The partial ordering of G2(2) nilpotent orbits matches the phase diagram of extremal black holes.

The study provides a geometric framework for understanding black hole extremality.

Abstract

We study extremal cohomogeneity one five-dimensional asymptotically flat black holes of minimal supergravity in terms of the geodesics generated by nilpotent elements of the Lie algebra g2(2) on the coset manifold G2(2)/SO(2,2). There are two branches of regular extremal black holes with these properties: (i) the supersymmetric BMPV branch, and (ii) the non-supersymmetric extremal branch. We show that both of these branches are reproduced by nilpotent SO(2,2)-orbits. Furthermore, we show that the partial ordering of nilpotent orbits of G2(2) is in one-to-one correspondence with the phase diagram of these extremal black holes.