Field redefinitions, Weyl invariance, and nature of mavericks

Understand

In the theories of gravity with non-minimally coupled scalar fields there are "mavericks" -- unexpected solutions with odd properties, e.g., black holes with scalar hair in theories with scalar potential bounded from below.

• Probably the most famous example is Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole solution in a theory with a scalar field conformally coupled to the gravity and with vanishing potential.
• Its existence naively violates no-hair conjecture without violating no-hair theorems because of the singular behavior of the scalar field at the horizon.
• Despite being discovered more than 40 years ago, nature of BBMB solution is still the subject of research and debate.