Fully resonant scalars on asymptotically AdS wormholes

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 ε −2 (where ε 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 ε −2 . arXiv:1903.08239v2 [hep-th] 19 Apr 2019 2 Note that this is not the conformal coupling since in general ξ conf = D−2 4(D−1) .

Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

“…The relevant dynamics underlying the AdS instability happens on time scales 1/ 2 for perturbations of amplitude , which is precisely the domain of validity of the resonant approximation to (29) and (30), making it very natural to appeal to the resonant approximation in this context. The idea to pursue this approach was briefly flashed already in [8], but it took a few years before it got implemented in practice.…”

“…The resonant approximation was introduced to studies of AdS instability problems in [17], primarily as an alternative approach to numerical work, and then given a fully analytic formulation in [20,21] (deriving a fully analytic form of gravitational AdS resonant systems is challenging on account of the complexity of gravitational nonlinearities). Our purpose here will be to review the work on resonant approximations to the AdS dynamics along the lines of [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The complexity of the resonant dynamics in AdS invites, furthermore, studies of simpler related systems, for example interacting scalars in nondynamical AdS backgrounds [32][33][34][35].…”

Time-periodicities in holographic CFTs

“…Resonances between the linear normal modes are what enables nonlinearities to exert significant influences on perturbations of arbitrarily small amplitudes, provided that one waits long enough. A selection of further studies of this type of nonlinear dynamics can be found in [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]; for a short review, 2 see [19].…”

Scalars on asymptotically locally AdS wormholes with $\mathcal{R}^{2}$ terms

“…It is interesting to note that for modes without angular momentum (n = 0) and ξ = 3/8 both potentials lead to a fully resonant, equispaced spectra, which might enhance the energy transfer between modes when non-linearities are included [32], as it happens in AdS.…”