Fully resonant scalars on asymptotically AdS wormholes

In this work, we show the existence of asymptotically anti-de Sitter (AdS) wormhole geometries in which the scalar probe has an equispaced, fully resonant spectrum, as that of a scalar on AdS spacetime, and explore its dynamics when nonlinearities are included. The spacetime is a solution of Einstein-Gauss-Bonnet theory with a single maximally symmetric vacuum. Introducing a nonminimal coupling between the scalar probe and the Ricci scalar remarkably leads to a fully resonant spectrum for a scalar field fulfilling reflective boundary conditions at both infinities. Applying perturbative methods, which are particularly useful for unveiling the dynamics at time scales of order μ-2 (where μ characterizes the amplitude of the initial perturbation), we observe both direct and inverse energy cascades between modes. This motivates us to explore the energy returns in the case in which the dynamics is dominated by a single mode. We find numerical and perturbative evidence that near-exact returns do exist in this regime. We also provide some comments on the fully backreracting case and provide a proof of the universality of the weakly nonlinear dynamics around AdS, in the context of Lovelock theories with generic couplings, up to times of order μ-2.