Phase transitions near black hole horizons

The Reissner-Nordström black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field. New stable black hole solutions then exist with greater entropy for fixed mass and charge than the Reissner-Nordström solution. In these new solutions, the scalar condenses to a non-zero value near the horizon. Various generalizations of these hairy black holes are discussed, and an attempt is made to characterize when black hole hair can occur.