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

Mariano Cadoni and Matteo Serra

Salvatore Mignemi

  • Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari - Cittadella Universitaria, 09042 Monserrato, Italy

  • Dipartimento di Matematica, Università di Cagliari and INFN, Sezione di Cagliari - viale Merello 92, 09123 Cagliari, Italy

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Phys. Rev. D 84, 084046 – Published 21 October, 2011

DOI: https://doi.org/10.1103/PhysRevD.84.084046

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 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.

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Phys. Rev. D 84, 084046– Published 21 October, 2011
  • Received 16 August 2011

© 2011 American Physical Society

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