# Information Transfer and Black Hole Evaporation via Traversable BTZ Wormholes

## TL;DR

This paper explores how traversable BTZ wormholes enable information transfer, linking black hole evaporation and quantum information concepts through dual conformal field theories and shockwave dynamics.

## Contribution

It provides a detailed construction of traversable BTZ wormholes via shockwaves, establishing bounds on information transfer and connecting wormhole traversability to black hole evaporation processes.

## Key findings

- Bound on information transfer through wormholes
- Delayed scrambling time due to negative energy shock waves
- Connection between traversability and the Page curve in black hole evaporation

## Abstract

We study traversable wormholes by considering the duality between BTZ black holes and two-dimensional conformal field theory on the thermofield double state. The BTZ black holes can be rendered traversable by a negative energy shock wave. Following Gao, Jafferis and Wall [1], we show that the negative energy shock wave is dual to the infinite boost limit of a specific double trace deformation which couples the left and right CFTs. We spell out the mechanism of information transfer through traversable BTZ wormholes, treating the backreaction of the message as a positive energy shockwave. The corresponding spacetime is that of colliding spherical shells in the BTZ black hole, which we explicitly construct. This construction allows us to obtain a bound on the amount of information that can be sent through the wormhole, which is consistent with previous work in the context of nearly $AdS_2$ gravity [2]. Consequently, we define a notion of traversibility of the wormhole and study it in the context of a multiple shock geometry. We argue that the time-dependence of traversibility in this geometry can be connected to certain aspects of the black hole evaporation process, such as the second half of the Page curve. Finally, we examine the claim that traversable wormholes are fast decoders. We find evidence for this by computing the scrambling time in the shockwave background and showing that it is delayed by the presence of the negative energy shock wave.