The uniqueness of the Bekenstein black hole

The general static, spherically symmetric, asymptotically flat solution of the Einstein equations coupled to a conformal scalar field is determined; it depends on three free parameters. One of the parameters is eliminated by the requirement that the solution admits a smooth horizon and no naked curvature singularities, leading to the black hole solution discovered by Bekenstein. Although the scalar field is unbounded on the horizon, this should not be considered as a physical pathology.