We discuss the role of the curvature in the physics of a black hole in curved space-time. We demonstrate that the black hole is dual to a Lorenzian massless scalar field in flat space-time. We show that the black hole is dual to a scalar field in flat space-time with a Lorenzian massless phase. We argue that the black hole is dual to a scalar field in flat space- and we prove that the scalar field is dual to a Lorenzian phase.