标题： 所有可分离的超对称AdS$_5$黑洞 显示英文标题

标题： All separable supersymmetric AdS$_5$ black holes

摘要： 我们考虑五维STU规范超引力中具有环面对称性的超对称黑洞解的分类。 这简化为基空间上的环面凯勒几何问题。 我们引入了一类可分离的环面凯勒表面，它统一了乘积环面、卡比塔斯环面和正交环面凯勒表面，同时还引入了一类相关的可分离2-形式。 我们证明，任何具有可分离凯勒基空间和麦克斯韦场的类时超对称环面解，在具有紧致（局部）球形横截面的视界之外，必须局部等距于已知的黑洞或其近视界几何结构。 证明的关键部分是对近视界区域的分析，该分析表明唯一的可能可分离凯勒基空间是卡比塔斯环面。 特别是，这也意味着我们之前针对最小规范超引力的黑洞唯一性定理适用于更大的可分离凯勒基空间类别。 显示英文摘要

摘要： We consider the classification of supersymmetric black hole solutions to five-dimensional STU gauged supergravity that admit torus symmetry. This reduces to a problem in toric K\"ahler geometry on the base space. We introduce the class of separable toric K\"ahler surfaces that unify product-toric, Calabi-toric and orthotoric K\"ahler surfaces, together with an associated class of separable 2-forms. We prove that any supersymmetric toric solution that is timelike, with a separable K\"ahler base space and Maxwell fields, outside a horizon with a compact (locally) spherical cross-section, must be locally isometric to the known black hole or its near-horizon geometry. An essential part of the proof is a near-horizon analysis which shows that the only possible separable K\"ahler base space is Calabi-toric. In particular, this also implies that our previous black hole uniqueness theorem for minimal gauged supergravity applies to the larger class of separable K\"ahler base spaces.