All separable supersymmetric AdS${}_5$ black holes

Abstract

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 Kähler geometry on the base space. We introduce the class of separable toric Kähler surfaces that unify product-toric, Calabi-toric and orthotoric Kähler surfaces, together with an associated class of separable 2-forms. We prove that any supersymmetric toric solution that is timelike, with a separable Kähler 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 Kähler 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 Kähler base spaces.

47 pages, 1 figure. v2: minor edits, published version

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