Squashing the Boundary of Supersymmetric AdS$_5$ Black Holes

TL;DR

This paper constructs new supersymmetric AdS$_5$ black hole solutions with arbitrary boundary squashing, revealing how boundary conditions influence horizon properties and providing insights into dual gauge theories.

Contribution

It introduces a family of supersymmetric black holes with arbitrary boundary squashing in five-dimensional supergravity, extending known solutions and exploring boundary-horizon relations.

Findings

Solution depends on two parameters: angular momentum and boundary squashing.

Boundary squashing is arbitrary but flows to a fixed value near the horizon.

Entropy formula involves angular momentum and Page charges, not holographic charges.

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.