No-hair theorems for black holes in the Abelian Higgs model

Abstract

Motivated by the study of holographic superconductors, we generalize no-hair theorems for minimally coupled scalar fields charged under an Abelian gauge field, in arbitrary dimensions and with arbitrary horizon topology. We first present a straightforward generalization of no-hair theorems for neutral scalar hair. We then consider the existence of extremal black holes with scalar hair, and in the case of horizons with zero or positive curvature, provide a bound on the mass and charge of the scalar field that are necessary for the scalar hair to develop.

12 pages. v2: expanded abstract, added references

References in corpus (12)

• Building an AdS/CFT superconductor
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Near-horizon symmetries of extremal black holes
• Holographic superconductivity in M-Theory
• Superconductors from Superstrings
• Colorful horizons with charge in anti-de Sitter space
• A classification of near-horizon geometries of extremal vacuum black holes
• The gravity dual to a quantum critical point with spontaneous symmetry breaking
• Extremal vacuum black holes in higher dimensions
• Electrically charged black hole with scalar hair
• Low-temperature behavior of the Abelian Higgs model in anti-de Sitter space
• Exact Gravity Dual of a Gapless Superconductor

Cited by in corpus (12)

• Hairy black holes and solitons in global AdS 5
• Small Hairy Black Holes in $Ad{S}_5\times S^5$
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Phase Transition to a Hairy Black Hole in Asymptotically Flat Spacetime
• Ultraspinning instability: the missing link
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime
• Extremal Hairy Black Holes
• Hairy charged Gauss-Bonnet solitons and black holes
• The Rich Structure of Gauss-Bonnet Holographic Superconductors
• A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time
• Formation of scalar hair on Gauss-Bonnet solitons and black holes