De Sitter black hole with a conformally coupled scalar field in four dimensions

A four-dimensional black hole solution of the Einstein equations with a positive cosmological constant coupled to a conformal scalar field is given. There is a curvature singularity at the origin, and the scalar field has a divergence inside the event horizon. The electrically charged solution, which has a fixed charge-to-mass ratio, is also found. The quartic self-interacting coupling constant becomes bounded in terms of Newton’s constant and the cosmological constant. The solution satisfies both dominant and the strong energy conditions.