TY - JOUR

T1 - Hairy black hole stability in AdS, quantum mechanics on the half-line and holography

AU - Anabalón, Andrés

AU - Astefanesei, Dumitru

AU - Oliva, Julio

N1 - Publisher Copyright:
© 2015, The Author(s).

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Black Holes

UR - http://www.scopus.com/inward/record.url?scp=84944460917&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2015)068

DO - 10.1007/JHEP10(2015)068

M3 - Article

AN - SCOPUS:84944460917

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 68

ER -