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 $\varepsilon^{-2}$.
Highlights
General Relativity (GR) in dimensions higher than 4 can be extended, still fulfilling the requirements of second-order field equations and diffeomorphism invariance
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
We have shown the existence of a spacetime with nontrivial topology on which the linear dynamics of a scalar probe turn out to be fully resonant, leading to a rich phenomenology when nonlinearities are included
Summary
General Relativity (GR) in dimensions higher than 4 can be extended, still fulfilling the requirements of second-order field equations and diffeomorphism invariance. In dimensions D ≥ 5, the precise combination of higher curvature terms can be added to the Einstein-Hilbert action, leading to second-order field equations [1]. These combinations are dimensional continuations of the Euler densities of the lower, even dimensions. Equispaced spectra play an important role in turbulent energy transfer leading to the nonperturbative AdS instability [14,15,16,17,18,19] These kind of fully resonant spectra lead to a rich phenomenology that appears in nonlinear models of different physical nature as in self-gravitating scalars on a spherical cavity in 3 þ 1 [20], on systems describing Bose-Einstein condensates [21], and vortex precession [22], as well as in the conformal dynamics on the Einstein universe [23]. We show that for an arbitrary Lovelock theory, provided the couplings are generic, the form of the equation for the infinite oscillators that control the dynamics in the TTF is universal
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