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We construct a family of asymptotically flat, rotating black holes withscalar hair and a regular horizon, within five dimensional Einstein's gravityminimally coupled to a complex, massive scalar field doublet. These solutionsare supported by rotation and have no static limit. They are described by theirmass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noethercharge $Q$, measuring the scalar hair. For vanishing horizon size the solutionsreduce to five dimensional boson stars. In the limit of vanishing Noethercharge density, the scalar field becomes point-wise arbitrarily small and thegeometry becomes, locally, arbitrarily close to that of a specific set ofMyers-Perry black holes (MPBHs); but there remains a global difference withrespect to the latter, manifest in a finite mass gap. Thus, the scalar hairnever becomes a linear perturbation of MPBHs. This is a qualitative differencewhen compared to Kerr black holes with scalar hair~\cite{Herdeiro:2014goa}.Whereas the existence of the latter can be anticipated in linear theory, fromthe existence of scalar bound states on the Kerr geometry (i.e. scalar clouds),the hair of these MPBHs is intrinsically non-linear.

Myers-Perry black holes with scalar hair and a mass gap