From black strings to black holes: nuttier and squashed AdS$_5$ solutions

TL;DR

This paper constructs new five-dimensional Einstein solutions, including deformations of AdS5 black strings, which serve as gravity duals for super-Yang-Mills theories in G"odel-type backgrounds and feature squashed black holes with complex topologies.

Contribution

It introduces novel deformations of AdS5 black strings, including Taub-NUT-AdS uplifted solutions and squashed black holes, expanding the landscape of known gravitational backgrounds.

Findings

Solutions are smooth deformations of AdS5 black strings.

Gravity duals for super-Yang-Mills in G"odel backgrounds are identified.

New squashed AdS black holes with complex topologies are constructed.

Abstract

We construct new solutions of the Einstein equations with negative cosmological constant in five spacetime dimensions. They smoothly emerge as deformations of the known AdS$_5$ black strings. The first type of configurations can be viewed as the $d=4$ Taub-NUT-AdS solutions uplifted to five dimensions, in the presence of a negative cosmological constant. We argue that these solutions provide the gravity dual for a ${\cal N}=4$ super-Yang-Mills theory formulated in a $d=4$ homogeneous G\"odel-type spacetime background. A different deformation of the AdS$_5$ black strings leads to squashed AdS black holes and their topological generalizations. In this case, the conformal infinity is the product of time and a circle-fibration over a base space that is a two-dimensional Einstein space.