Construct hairy rotating black holes in the conifold truncation

Construct numerical hairy black-hole solutions in the AdS$_5\times T^{1,1}$ conifold truncation and determine whether they are unstable to charge superradiance, as occurs for the known hairy solutions in the AdS$_5\times S^5$ truncation.

Background

The paper studies charge-superradiant instabilities using probe D3-branes in AdS$_5\times T^{1,1}$ and assumes, by analogy with the maximally symmetric AdS$_5\times S^5$ case, that hairy black holes in the conifold truncation would themselves be unstable to charge superradiance. However, the authors note that no corresponding hairy rotating solutions have yet been constructed. Establishing these solutions and testing their stability would determine whether the probe-brane endpoint picture applies beyond the known five-sphere truncation.