Collisions of localized shocks and quantum circuits

Abstract

We study collisions between localized shockwaves inside a black hole interior. We give a holographic boundary description of this process in terms of the overlap of two growing perturbations in a shared quantum circuit. The perturbations grow both exponentially as well as ballistically. Due to a competition between different physical effects, the circuit analysis shows dependence on the transverse locations and exhibits four regimes of qualitatively different behaviors. On the gravity side we study properties of the post-collision geometry, using exact calculations in simple setups and estimations in more general circumstances. We show that the circuit analysis offers intuitive and surprisingly accurate predictions about gravity computations involving non-linear features of general relativity.

Bouncing inside the horizon and scrambling delays

“…Assuming the same connection between the number of healthy gates and the volume of the postcollision region as discussed above, we expect a plateau in the post-collision region spacetime volume as a function of ∆t [9]. As we explain in the next section, this is indeed what we find.…”

“…Let us now consider two perturbations (one sent in from the left and one from the right) that meet inside the black hole. It was proposed in [9] that one can compare the scrambling times of these two perturbations by computing the four-volume of the post-collision region, and seeing how it varies as one changes the time at which one perturbation is introduced. We construct the solution with two null shells, one charged and one neutral, and compute the volume of the post-collision region.…”

“…Note that in this section we define ∆t to be dimensionless 9. It is important to only do this approximation after taking the derivative as otherwise one will neglect contributions which are non-negligible for certain time configurations.…”

The black hole interior from non-isometric codes and complexity

“…It would be interesting to apply the dynamical evolution of the previous section to the two-sided black holes we consider here. We expect that the analysis in [87][88][89] of meetings in the black hole interior could be re-interpreted in this context.…”