We investigate the possibility of dressing a four-dimensional black hole with
classical scalar field hair which is non-minimally coupled to the space-time
curvature. Our model includes a cosmological constant but no self-interaction
potential for the scalar field. We are able to rule out black hole hair except
when the cosmological constant is negative and the constant governing the
coupling to the Ricci scalar curvature is positive. In this case, non-trivial
hairy black hole solutions exist, at least some of which are linearly stable.
However, when the coupling constant becomes too large, the black hole hair
becomes unstable.Comment: 17 pages, 7 figures, uses iopart.cls. Minor changes, accepted for
publication in Classical and Quantum Gravit