gr-qc/9602057 We prove three theorems in general relativity which rule out classical scalar hair of static , spherically symmetric , possibly electrically charged black holes .
We first generalize Bekenstein ’ s no–hair theorem for a multiplet of minimally coupled real scalar fields with not necessarily quadratic action to the case of a charged black hole .
We then use a conformal map of the geometry to convert the problem of a charged ( or neutral ) black hole with hair in the form of a neutral self–interacting scalar field nonminimally coupled to gravity to the preceding problem , thus establishing a no–hair theorem for the cases with nonminimal coupling parameter \xi < 0 or \xi \geq { 1 \over 2 } .
The proof also makes use of a causality requirement on the field configuration .
Finally , from the required behavior of the fields at the horizon and infinity we exclude hair of a charged black hole in the form of a charged self–interacting scalar field nonminimally coupled to gravity for any \xi .