Neumann boundary conditions in anti-de Sitter space admit non-collapsing, multi-mode scalar solutions with arbitrarily small amplitude despite a fully resonant spectrum.
On the AdS stability problem
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abstract
We discuss the notion of stability and the choice of boundary conditions for AdS-type space-times and point out difficulties in the construction of Cauchy data which arise if reflective boundary conditions are imposed.
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New islands of stability with double-trace deformations
Neumann boundary conditions in anti-de Sitter space admit non-collapsing, multi-mode scalar solutions with arbitrarily small amplitude despite a fully resonant spectrum.