Spherical black holes cannot support scalar hair

The static spherically symmetric “black hole solution” of the Einstein conformally invariant massless scalar field equations presented by Bekenstein and by Bocharova, Bronikov, and Melnikov is critically examined. It is shown that the stress energy tensor is ill defined at the horizon as a result of the distributional character of the scalar field. Consequently, the configuration fails to represent a genuine black hole solution. With the removal of this solution as a counterexample to the no hair conjecture, we argue that the following appears to be true: Spherical black holes cannot carry any kind of classical scalar hair.