Hairy black hole stability in AdS, quantum mechanics on the half-line and holography

  • Andrés Anabalón
  • Dumitru Astefanesei
  • Julio Oliva
Open Access
Regular Article - Theoretical Physics


We consider the linear stability of 4-dimensional hairy black holes with mixed boundary conditions in Anti-de Sitter spacetime. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged \( \mathcal{N}=8 \) supergravity in four dimensions, m 2 = −2l −2. It is shown that the Schrödinger operator on the half-line, governing the S 2, H 2 or \( {\mathbb{R}}^2 \) invariant mode around the hairy black hole, allows for non-trivial self-adjoint extensions and each of them corresponds to a class of mixed boundary conditions in the gravitational theory. Discarding the self-adjoint extensions with a negative mode impose a restriction on these boundary conditions. The restriction is given in terms of an integral of the potential in the Schrödinger operator resembling the estimate of Simon for Schrödinger operators on the real line. In the context of AdS/CFT duality, our result has a natural interpretation in terms of the field theory dual effective potential.


Black Holes AdS-CFT Correspondence 


Open Access

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© The Author(s) 2015

Authors and Affiliations

  • Andrés Anabalón
    • 1
  • Dumitru Astefanesei
    • 2
  • Julio Oliva
    • 3
  1. 1.Departamento de Ciencias, Facultad de Artes Liberales y Facultad de Ingeniería y CienciasUniversidad Adolfo IbáñezViña del MarChile
  2. 2.Instituto de FísicaPontificia Universidad Católica de ValparaísoValparaísoChile
  3. 3.Departamento de FísicaUniversidad de ConcepciónConcepciónChile

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