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) .

In this paper we study the propagation of a probe scalar on an asymptotically locally AdS wormhole solution of Einstein-Gauss-Bonnet theory in five dimensions. The radial coordinate ρ connects both asymptotic regions located at ρ → ±∞. The metric is characterized by a single integration constant ρ 0 and the wormhole throat is located at ρ = 0. In the region 0 < ρ < ρ 0 , both the gravitational pull as well as the centrifugal contributions to the geodesic motion point in the same direction and therefore they cannot balance. We explore the consequences of the existence of this region on the propagation of a scalar probe. The cases with ρ 0 = 0 as well as the limit ρ 0 → +∞ lead to exactly solvable differential eigenvalue problems, with shape-invariant potentials of the Rosen-Morse and Scarf family, respectively. Here, we numerically obtain the normal modes of a scalar field when ρ 0 = 0, with reflecting boundary conditions at both asymptotic regions. We also explore the effect of a non-minimal coupling between the scalar curvature and the scalar field.Remarkably, there is a particular value of the non-minimal coupling parameter that leads to fully resonant spectra in the limit of vanishing ρ 0 as well as when ρ 0 → +∞, for purely radial modes.

In this work we study the phase transitions between the planar charged AdS black hole and the planar charged soliton. The planar soliton is obtained as a double analytic continuation of the charged black hole metric, which also involves analytically continuing the electric charge. We show that there are phase transitions between both solutions depending on the electric potential, magnetic flux and temperature. The analysis is carried out in the Grand-Canonical ensemble.

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