We prove that any supersymmetric solution to five-dimensional minimal gauged supergravity with SU (2) symmetry, that is timelike outside an analytic horizon, is a Gutowski-Reall black hole or its near-horizon geometry. The proof combines a delicate near-horizon analysis with the general form for a Kähler metric with cohomogeneity-1 SU (2) symmetry. We also prove that any timelike supersymmetric soliton solution to this theory, with SU (2) symmetry and a nut or a complex bolt, has a Kähler base with enhanced U (1) × SU (2) symmetry, and we exhibit a family of asymptotically AdS 5 /Z p solitons for p ≥ 3 with a bolt in this class.
We consider the classification of supersymmetric AdS(5) black hole solutions to minimal gauged supergravity that admit a torus symmetry. This problem reduces to finding a class of toric Kähler metrics on the base space, which in symplectic coordinates are determined by a symplectic potential. We derive the general form of the symplectic potential near any component of the horizon or axis of symmetry, which determines its singular part for any black hole solution in this class, including possible new solutions such as black lenses and multi-black holes. We find that the most general known black hole solution in this context, found by Chong, Cvetic, Lü and Pope (CCLP), is described by a remarkably simple symplectic potential. We prove that any supersymmetric and toric solution that is timelike outside a smooth horizon, with a Kähler base metric of Calabi type, must be the CCLP black hole solution or its near-horizon geometry.
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