# Fully resonant scalars on asymptotically AdS wormholes

## TL;DR

This paper demonstrates the existence of asymptotically AdS wormhole geometries with a scalar field spectrum that is fully resonant, similar to AdS spacetime, and explores their nonlinear dynamics and energy transfer behaviors.

## Contribution

It introduces a new class of asymptotically AdS wormhole solutions with fully resonant scalar spectra and analyzes their nonlinear evolution and energy cascade phenomena.

## Key findings

- Existence of asymptotically AdS wormholes with fully resonant scalar spectra.
- Observation of energy cascades and near-exact energy returns in nonlinear dynamics.
- Universal weakly nonlinear behavior in Lovelock theories near AdS.

## Abstract

In this work we show the existence of asymptotically AdS wormhole geometries where the scalar probe has an equispaced, fully resonant spectrum, as that of a scalar on AdS spacetime, and explore its dynamics when non-linearities are included. The spacetime is a solution of Einstein-Gauss-Bonnet theory with a single maximally symmetric vacuum. Introducing a non-minimal 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 $\varepsilon^{-2}$ (where $\varepsilon$ 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 non-linear dynamics around AdS, in the context of Lovelock theories with generic couplings, up to times of order $\varepsilon^{-2}$.