Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field

We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. These solutions include: (1) four- or generic ($d+2$)-dimensional solutions with planar, spherical or hyperbolic horizon topology; (2) solutions with anti-de Sitter, domain wall and Lifshitz asymptotics; (3) solutions interpolating between an anti-de Sitter spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.