In this work, we analyze the necessary conditions for a nonlinear AdS-type instability in the gravity-scalar field system. In particular, we discuss the necessary conditions for a cascade of energy to higher modes by applying results in KAM theory. Our analytical framework explains numerical observations of instability of spacetimes even when the spectrum is only asymptotically resonant, and the fact that a minimum field amplitude is needed to trigger it. Our framework can be applied for similar stability analyses of fields in (locally) asymptotically AdS spacetimes. We illustrate this with the example of the AdS soliton. Further, we conjecture on the possible reasons for quasiperiodic behaviour observed in perturbations of AdS spacetime. Certain properties of the eigenfunctions of the linear system dictate whether there will be localization in space leading to black hole formation. These properties are examined using the asymptotics of Jacobi polynomials. Finally we discuss recent results on the AdS instability in Einstein-Gauss-Bonnet gravity in light of our work.

Motivated by recent studies of nonlinear perturbations of asymptotically anti-de Sitter spacetimes, we study gravitational perturbations of (n + 2) dimensional Minkowski spacetime with a spherical Dirichlet wall. By considering the tensor, vector and scalar perturbations on the n sphere, we present simplified nonhomogeneous equations at arbitrary order in weakly nonlinear perturbation theory for each sector. A suitable choice of perturbative variables is required at higher orders to simplify the expression for the boundary conditions and to expand the variables in terms of linear order eigenfunctions. Finally we comment on the nonlinear stability of the system. Some of the tools used can easily be generalized to study nonlinear perturbations of anti-de Sitter spacetime.

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The two-nucleon interaction, via the exchange of scalar mesons, is examined in a nonperturbative manner. 'Schrodinger' equations are derived, and nonlocal potentials arise naturally. Both scattering and bound states are examined. A half-off-shell T matrix is obtained, and corresponding phase shifts are evaluated. In the bound state, a variational calculation is employed to determine the coupling constant.Onexamine, sans avoir recours a la methode de perturbation, I'interaction entre deux nucleons par tchange de mesons scalaires. Des equations de 'Schrodinger' sont etablies, et des potentiels non locaux apparaissent naturellement. Les Ctats de diffusion aussi bien que 1'Ctat lie sont examines. Une demi-extension de la matrice T est obtenue, et les dtphasages correspondants sont Cvalues. Dans le cas de I'etat lie, on utilise un calcul variationnel pour dkterminer la constante de couplage.[Traduit par le journal]Can. J . Phys.. 54.322 (1976)

An earlier paper examined the role of scalar mesons in the nucleon–nucleon interaction. A more realistic model, with pseudoscalar mesons, is studied here. Unlike previous treatments of this problem, this approach seems to yield more repulsion than would be required to reproduce experimental data. Calculations are performed on the spin singlet, isospin triplet state; a brief discussion of the deuteron channel and the resulting potentials is also included.