Extremal solutions of the S3 model and nilpotent orbits of G2(2)

TL;DR

This paper classifies extremal black hole solutions in the S3 model using group theory, identifying distinct orbits and constructing new black string solutions with potential links to black rings.

Contribution

It provides a group-theoretical classification of extremal solutions in the S3 model and introduces new extremal black string solutions, expanding understanding of supergravity black objects.

Findings

Identified six nilpotent K-orbits corresponding to extremal solutions.

Three orbits are supersymmetric, one non-supersymmetric, two unphysical.

Constructed new extremal black strings and analyzed their properties.

Abstract

We study extremal black hole solutions of the S3 model (obtained by setting S=T=U in the STU model) using group theoretical methods. Upon dimensional reduction over time, the S3 model exhibits the pseudo-Riemannian coset structure G/K with G=G2(2) and K=SO(2,2). We study nilpotent K-orbits of G2(2) corresponding to non-rotating single-center extremal solutions. We find six such distinct K-orbits. Three of these orbits are supersymmetric, one is non-supersymmetric, and two are unphysical. We write general solutions and discuss examples in all four physical orbits. We show that all solutions in supersymmetric orbits when uplifted to five-dimensional minimal supergravity have single-center Gibbons-Hawking space as their four-dimensional Euclidean hyper-K\"ahler base space. We construct hitherto unknown extremal (supersymmetric as well as non-supersymmetric) pressureless black strings of minimal five-dimensional supergravity and briefly discuss their relation to black rings.