Rotating tensor-multiscalar black holes with two scalars

We construct hairy black hole solutions in a particular set of tensor-multi-scalar theories of gravity for which the target-space admits a Killing vector field with periodic flow that is furthermore the generator of a one-parameter family of point transformations which leave the whole theory invariant. As for black holes with scalar hair in general relativity, these must be rotating objects as the scalarization arises from superradiant instability. We analyze the most fundamental rotating solutions (winding number $m=1$) in five theories which differ from each other by the value of the Gauss curvature of the target-space. The domain of existence of these solutions is investigated, as well as their hairyness, horizon area and deformation factor.