Traversable wormhole with double trace deformations via gravitational shear and sound channels

Abstract

We investigate how non-local gravitational couplings from double-trace deformation between two asymptotic boundaries of an AdS$_5$ black brane can lead to the violation of the Averaged Null Energy Condition (ANEC). The first-order gravitational perturbations backreact with the background metric at second-order, creating a wormhole opening. The wormhole becomes traversable in both the gravitational shear and sound channels within the hydrodynamic approximation. This shows that dynamical metric perturbations can facilitate information transfer in a purely gravitational setting, with the emergence of $G_N$ indicating the gravitational origin. For the shear channel, we consider three different coupling configurations, whereas for the sound channel, we vary both the speed of sound and the attenuation constant, as these parameters control the wormhole traversability. Furthermore, we obtain late-time power-law behavior in the ANEC using fitting function and present a generalization that applies to both shear and sound channels. Due to its propagating nature, the sound channel exhibits late-time power-law remnants at low sound speed similar to the vector diffusive probes, but it prefers an exponential decay at higher sound speed similar to the scalar non-diffusive probes, as the power-law exponent weakened with increasing sound speed. For superluminal sound channels, the wormhole opens for an extremely brief duration at late insertion times, rendering it non-traversable.

Figures (9)

• Figure 1: Normalized energy-momentum tensor versus $V$ for various values of the insertion time $V_0$ for Case I (top-left), Case II (top-right), and Case III (bottom). Here, we use $\bar{a}=-1$ and $u_{\text{max}}=1/2$.
• Figure 2: The normalized ANEC as a function of insertion time $V_0$ for Case I, II, and III that ends at $V=+\infty$. Here, we use $\bar{a}=-1$ and $u_{\text{max}}=1/2$. We can see, the earlier the deformation is turned on the more traversable the wormhole shown by the increasing negative value of ANEC. Note that the insertion time $V_0=1$ corresponds to insertion time $t_0=0$, where the wormhole becomes most traversable.
• Figure 3: The plot of the normalized $\langle\hat{T}_{VV}^{(2)}\rangle$ versus $V$ (left) and the ANEC versus $V_0$ (right) for the sound channels with $u_{\text{max.}}=1/2$.
• Figure 4: Plot of ANEC versus $V_0$ for various values of $u_{\text{max.}}$ in sound channels. The markers indicate the values of $V_0$ corresponding to the minimum ANEC for each $u_{\text{max.}}$.
• Figure 5: The plot of ANEC versus $V_0$ for various values of the ratio $\alpha\equiv\frac{2\pi \bar{\Gamma}_s}{v_s^2}$ in sound channel. In this plot, we choose $u_{\text{max.}}=1/2$.