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In the theories of gravity with non-minimally coupled scalar fields there are"mavericks" -- unexpected solutions with odd properties, e.g., black holes withscalar hair in theories with scalar potential bounded from below. Probably themost famous example is Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) blackhole solution in a theory with a scalar field conformally coupled to thegravity and with vanishing potential. Its existence naively violates no-hairconjecture without violating no-hair theorems because of the singular behaviorof the scalar field at the horizon. Despite being discovered more than 40 yearsago, nature of BBMB solution is still the subject of research and debate. Weargue here that the key in understanding nature of maverick solutions is theproper choice of field redefinition schemes in which the solutions are regular.It appears that in such "regular" schemes mavericks have different physicalinterpretations, in particular they are not elementary but composite objects.For example, BBMB solution is not an extremal black hole but a collection of awormhole and a naked singularity. In the process we show that Weyl-invariantformulation of gravity is a perfect tool for such analyzes.

Field redefinitions, Weyl invariance, and nature of mavericks