Staticity Theorem for Non-Rotating Black Holes with Non-Minimally   Coupled Self-Interacting Scalar Fields
  Self-interacting scalar field configurations which are non-minimally coupled ($\zeta\neq0$) to the gravity of a strictly stationary black hole with non-rotating horizon are studied. It is concluded that for analytical configurations the corresponding domain of outer communications is static. 
Eloy Ay\'on-Beato