Traversable Wormholes via a Double Trace Deformation

TL;DR

This work shows that coupling the two boundaries of an eternal BTZ black hole via a relevant double-trace deformation induces a negative averaged null energy that backreacts to render the Einstein-Rosen bridge traversable, without violating causality. The authors compute the linear-order bulk two-point function, demonstrate a negative T_UU on the horizon and a negative ∫ dU T_UU for 0<Δ<1, and analyze the corresponding holographic energy-entropy changes. They interpret the traversable wormhole in the ER=EPR framework and as a dynamical quantum teleportation-like process, while relating the bulk effect to shifts in the quantum extremal surface and generalized entropy. The results provide a UV-complete example of traversable wormholes in AdS/CFT and illuminate how boundary couplings can realize information-transfer channels through nontrivial bulk geometries.

Abstract

After turning on an interaction that couples the two boundaries of an eternal BTZ black hole, we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description.

Figures (4)

• Figure 1.1: (a) is the Penrose diagram and (b) shows the Kruskal coordinates of the eternal black hole
• Figure 3.1: (a) shows the null energy along the horizon when the interaction is turned on at $U=U_{0}=1$ and never shut off, with our choice for the sign of the coupling $h$; (b) shows the case where it is turned on at $U=U_{0}=1$ and turned off at $U=U_{f}=2$. In both cases, $h=1$. We see clearly in both (a) and (b) that $T_{UU}$ becomes negative after turn-on; in (b) $T_{UU}$ becomes positive after turn-off. Blue is for $\Delta=0.1$; yellow is for $\Delta=0.2$; green is for $\Delta=0.4$; pink is for $\Delta=0.6$; purple is for $\Delta=0.8$
• Figure 3.2: $\int dUT_{UU}$ as a function of $\Delta$; blue is for $U_{0}=1$; yellow is for $U_{0}=2$; green is for $U_{0}=1$ and $U_{f}=2$
• Figure 4.1: The throat size is $\Delta V\sim h$. The red thick interval on the boundary is the duration of the deformation beginning at $t_0$ and ending at $t_f$. The metric in the light yellow region is unchanged and only that of the white region will have a nonzero backreaction correction. The orange thick curve is the future event horizon and the grey thick curve is the past event horizon. $E_1$ is the original bifurcation surface. $E_2$ is the location where the right and left future horizons cross. The magenta curve is a null ray that passes through wormhole, deviating to right boundary.