Exact Black-Hole Solution With Self-Interacting Scalar Field

Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair. The symmetric interaction potential has both signs and a triple-well shape with a smooth but non-analytic minimum at vanishing field. We present numerical data as well as double series expansions around spatial infinity.