  We consider self-interacting scalar fields coupled to gravity. Two classes of
exact solutions to Einstein's equations are obtained: the first class
corresponds to the minimal coupling, the second one to the conformal coupling.
One of the solutions is shown to describe a formation of a black hole in a
cosmological setting. Some properties of this solution are described. There are
two kinds of event horizons: a black hole horizon and cosmological horizons.
The cosmological horizons are not smooth. There is a mild curvature
singularity, which affects extended bodies but allows geodesics to be extended.
It is also shown that there is a critical value for a parameter on which the
solution depends. Above the critical point, the black hole singularity is
hidden within a global black hole event horizon. Below the critical point, the
singularity appears to be naked. The relevance to cosmic censorship is
discussed.
