Hairy black hole stability in AdS, quantum mechanics on the half-line and holography
Anabalon
A
author
Astefanesei
D
author
Oliva
J
author
2015
English
We consider the linear stability of 4-dimensional hairy black holes with mixed boundary conditions in Anti-de Sitter spacetinie. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged N = 8 supergravity in four dimensions, m(2) = -2l(-2). It is shown that the Schrodinger operator on the half-line, governing the S-2, H-2 or R-2 invariant mode around the hairy black hole, allows for nontrivial 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 Schrodinger operator resembling the estimate of Simon for Schrodinger 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
WOS:000363555500003
exported from refbase (show.php?record=543), last updated on Fri, 04 Dec 2015 08:03:19 -0300
text
files/543_Anabalon_etal2015.pdf
10.1007/JHEP10(2015)068
Anabalon_etal2015
Journal Of High Energy Physics
J. High Energy Phys.
2015
Springer
continuing
periodical
academic journal
10
15 pp
1029-8479