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arXiv · 1004.5242

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

Sung-Soo Kim·Josef Lindman Hörnlund·Jakob Palmkvist·Amitabh Virmani
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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-Kähler 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.

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Sung-Soo Kim, Josef Lindman Hörnlund, Jakob Palmkvist, Amitabh Virmani. 2010-09-25. Extremal solutions of the S3 model and nilpotent orbits of G2(2). https://doi.org/10.1007/jhep08(2010)072

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