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

Andrés Anabalón, Dumitru Astefanesei, Julio Oliva

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Abstract: 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 N=8 supergravity in four dimensions, m2 = −2l−2. It is shown that the Schrödinger operator on the half-line, governing the S2, H2 or ℝ2 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.

Original languageEnglish
Article number68
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2015


  • AdS-CFT Correspondence
  • Black Holes


Dive into the research topics of 'Hairy black hole stability in AdS, quantum mechanics on the half-line and holography'. Together they form a unique fingerprint.

Cite this