Modified No-hair Conjecture and the Limiting Process

It is argued that the Schwarzschild black hole solution follows as a unique limit of the Brans-Dicke Class I solutions, provided the correct iterated limit is taken. Such a uniqueness is essential for the validity of a recent version of the no-hair conjecture. A non-trivial modification to this version is proposed in order to exclude Brans-Dicke Class IV solutions which appear to represent scalar hair black holes in general.