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Title: 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 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.

Authors:
; ;  [1]
  1. Dipartimento di Fisica, Universita di Cagliari and INFN, Sezione di Cagliari - Cittadella Universitaria, 09042 Monserrato (Italy)
Publication Date:
OSTI Identifier:
21607929
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 84; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.84.084046; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANTI DE SITTER SPACE; ASYMPTOTIC SOLUTIONS; BLACK HOLES; EINSTEIN-MAXWELL EQUATIONS; EXACT SOLUTIONS; FIELD EQUATIONS; FOUR-DIMENSIONAL CALCULATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; INTERACTIONS; MANY-DIMENSIONAL CALCULATIONS; METRICS; QUANTUM FIELD THEORY; SCALAR FIELDS; SPACE-TIME; SPHERICAL CONFIGURATION; SYMMETRY; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS; CONFIGURATION; EQUATIONS; FIELD THEORIES; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; MATHEMATICS; RELATIVITY THEORY; SPACE

Citation Formats

Cadoni, Mariano, Serra, Matteo, Mignemi, Salvatore, and Dipartimento di Matematica, Universita di Cagliari and INFN, Sezione di Cagliari - viale Merello 92, 09123 Cagliari. Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. United States: N. p., 2011. Web. doi:10.1103/PHYSREVD.84.084046.
Cadoni, Mariano, Serra, Matteo, Mignemi, Salvatore, & Dipartimento di Matematica, Universita di Cagliari and INFN, Sezione di Cagliari - viale Merello 92, 09123 Cagliari. Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. United States. doi:10.1103/PHYSREVD.84.084046.
Cadoni, Mariano, Serra, Matteo, Mignemi, Salvatore, and Dipartimento di Matematica, Universita di Cagliari and INFN, Sezione di Cagliari - viale Merello 92, 09123 Cagliari. Sat . "Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field". United States. doi:10.1103/PHYSREVD.84.084046.
@article{osti_21607929,
title = {Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field},
author = {Cadoni, Mariano and Serra, Matteo and Mignemi, Salvatore and Dipartimento di Matematica, Universita di Cagliari and INFN, Sezione di Cagliari - viale Merello 92, 09123 Cagliari},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.84.084046},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 84,
place = {United States},
year = {2011},
month = {10}
}