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

TL;DR

This paper introduces a method for finding exact static solutions in Einstein and Einstein-Maxwell gravity coupled to a scalar field with AdS asymptotics, revealing new black hole solutions and a no-hair theorem.

Contribution

The authors develop a general approach to obtain exact solutions and prove a new no-hair theorem for hairy black holes in these theories.

Findings

Derived broad classes of static solutions with various horizon topologies.

Found solutions with AdS, domain wall, and Lifshitz asymptotics.

Identified solutions interpolating between AdS and Lifshitz or domain wall spacetimes.

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.