Numerical evidence against black holes with non-minimally coupled scalar hair

We search numerically for asymptotically flat, static and spherically symme tric black hole configurations in a system which consists of a real scalar field non-minimally coupled to gravity. This issue has been analysed previo usly, assuming external considerations to the theory which, as we explain, limit the generality of the analysis. We present a method that is useful fo r obtaining initial conditions for numerical analysis. Our results narrow t he range in which one can find black hole configurations without considerin g any requirements external to the theory.