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

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.Comment: 17 pages, 2 figures; v2 two minus sign typos in appendix A equation (A.3) corrected, no other change