Rotating stealth black holes with a cohomogeneity$$-1$$ metric

Abstract In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the field. A rotating stealth black hole solution is constructed where metric given by Myers–Perry spacetime with equal momenta field identified Hamilton–Jacobi potential. This nontrivial has an extra hair associated rest mass test particle, does not require any fine tuning coupling functions theory. Interestingly enough, show disformal transformation, generated this field, constant degree disformality, leaves invariant (up diffeomorphisms) momenta. means along disformality parameter, can be consistently absorbed into further redefinitions single angular parameter disformed metric. These results are extended in higher odd for which all equal. The key invariance under transformation mainly cohomogeneity $$-1$$ - 1 character Starting from observation, class metrics arbitrary dimension, list conditions ensuring remain kinetic term. extension Kerr+-de Sitter case also considered it shown solutions may exist provided some