Event horizons in static scalar-vacuum space-times

The following theorem is established. Every zero-mass scalar field which is gravitationally coupled, static and asymptotically flat, becomes singular at a simply-connected event horizon. In the special case where the gravitational coupling of the scalar energy density is neglected, the solutions are computed explicitly. Some properties of the singular event horizons are discussed, and a brief mention of related work with non-static scalar fields is given.