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

Abstract

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 AdS, domain wall and Lifshitz asymptotics; 3) solutions interpolating between an AdS spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.

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Cited by in corpus (21)

• Charged black hole with a scalar hair in (2+1) dimensions
• Phase transition and hyperscaling violation for scalar Black Branes
• Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes
• Asymptotically flat black holes sourced by a massless scalar field
• Constructing black holes in Einstein-Maxwell-scalar theory
• Holographic entanglement entropy in the nonconformal medium
• Bound orbits near scalar field naked singularities
• Bulk Viscosity in Holographic Lifshitz Hydrodynamics
• Non-conformal Hydrodynamics in Einstein-dilaton Theory
• Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity
• Transport in non-conformal holographic fluids
• Sine-Gordon solitonic scalar stars and black holes
• Anti-de Sitter massless scalar field spacetimes in arbitrary dimensions
• On black holes with scalar hairs
• Einstein-Maxwell gravity coupled to a scalar field in 2+1-dimensions
• Double-bounce domain-wall in Einstein-Yang-Mills-Scalar black holes
• Dark Energy from holographic theories with hyperscaling violation
• Inflation as de Sitter instability
• Holographic renormalization in dense medium
• On black hole thermodynamics with a momentum relaxation
• Black brane solutions of Einstein-Maxwell-scalar theory with Liouville potential