Squashing the Boundary of Supersymmetric AdS$_5$ Black Holes

Abstract

We construct new supersymmetric black holes in five-dimensional supergravity with an arbitrary number of vector multiplets and Fayet-Iliopoulos gauging. These are asymptotically locally AdS$_5$ and the conformal boundary comprises a squashed three-sphere with $\text{SU}(2)\times \text{U}(1)$ symmetry. The solution depends on two parameters, of which one determines the angular momentum and the Page electric charges, while the other controls the squashing at the boundary. The latter is arbitrary, however in the flow towards the horizon it is attracted to a value that only depends on the other parameter of the solution. The entropy is reproduced by a simple formula involving the angular momentum and the Page charges, rather than the holographic charges. Choosing the appropriate five-dimensional framework, the solution can be uplifted to type IIB supergravity on $S^5$ and should thus be dual to $\mathcal{N}=4$ super Yang-Mills on a rotating, squashed Einstein universe.