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 Khler 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 Khler base with enhanced U(1) SU(2) symmetry, and we exhibit a family of asymptotically Ad solitons for p ⩾ 3 with a bolt in this class.

中文翻译：

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具有 SU(2) 对称性的超对称 AdS5 黑洞的唯一性

我们证明了具有SU (2) 对称性的五维最小测量超重力的任何超对称解，即解析视界外的类时，是古托夫斯基-真实黑洞或其近视界几何。该证明将精细的近水平分析与具有同质性 1 SU (2) 对称性的Khler 度量的一般形式相结合。我们还证明了该理论的任何类时超对称孤子解，具有SU (2) 对称性和螺母或复杂螺栓，具有增强U (1) SU (2) 对称性的 Khler 基，并且我们展示了一个渐近族p ⩾ 3 的广告孤子，在这个类中有一个螺栓。