2009/11/18 by Mariano Cadoni, M. Cadoni, Paolo Pani +3
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology and Gravitation Theories #Geometry #Mathematical physics #Mathematics #Mechanics #Noncommutative and Quantum Gravity Theories #Physics #Scalar (mathematics) #Scalar field #Vortex #hep-th
paper · pdf · doi:10.1007/jhep01(2010)091
published as JHEP 1001:091,2010 · 12 pages, 2 figures
arxiv created 2009/11/18 · openalex publication_date 2010/01/01 · arxiv updated 2010/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate three-dimensional (3D) Anti-de Sitter (AdS) gravity coupled to a complex scalar field ϕwith self-interaction potential V(|ϕ|). We show that the mass of static, rotationally symmetric, AdS black hole with scalar hairs is determined algebraically by the scalar charges. We recast the field equations as a linear system of first order differential equations. Exact solutions, describing 3D AdS black holes with real spherical scalar hairs and vortex-black hole solutions are derived in closed form for the case of a scalar field saturating the Breitenlohner-Freedman (BF) bound and for a scalar field with asymptotic zero mass. The physical properties of these solutions are discussed. In particular, we show that the vortex solution interpolates between two different AdS3 vacua, corresponding respectively to a U(1)-symmetry-preserving maximum and to a symmetry-breaking minimum of the potential V.