Uniqueness of supersymmetric AdS${}_5$ black holes with $SU(2)$ symmetry

Abstract

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 $U(1)\times SU(2)$ symmetry, and we exhibit a family of asymptotically AdS${}_5/{\mathbb{Z}}_p$ solitons for $p\ge 3$ with a bolt in this class.

33 pages. v2: minor edits, published version

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• Supersymmetric asymptotically locally AdS${}_5$ gravitational solitons
• Rotating black holes with Nil or SL(2,$\mathbb{R}$) horizons
• Uniqueness of extremal charged black holes in de Sitter
• All separable supersymmetric AdS${}_5$ black holes