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We investigate stationary rotationally symmetric solutions of a particulartruncation of Horndeski theory in three dimensions, including a non-minimalscalar kinetic coupling to the curvature. After discussing the special case ofa vanishing scalar charge, which includes most of the previously knownsolutions, we reduce the general case to an effective mechanical model in athree-dimensional target space. We analyze the possible near-horizon behaviors,and conclude that black hole solutions with degenerate horizons and constantcurvature asymptotics may exist if the minimal and non-minimal scalar couplingconstants have the same sign. In a special case, we find a new analyticrotating black hole solution with scalar hair and degenerate horizon. This isgeodesically and causally complete, and asymptotic to the extreme BTZ metric.We also briefly discuss soliton solutions in another special case.

Hairy black hole solutions in a three-dimensional Galileon model