Black holes and the butterfly effect

TL;DR

This paper investigates how small perturbations in a holographic black hole setup can lead to drastic changes in correlations, illustrating the butterfly effect in strongly coupled quantum systems and its implications for quantum gravity debates.

Contribution

It demonstrates how early infalling quanta create shock waves in the bulk geometry, affecting correlations and providing insights into chaos and the firewall controversy.

Findings

Small perturbations cause significant correlation destruction.

Shock wave formation is linked to early quanta blueshift.

Results relate to quantum chaos and black hole information paradox.

Abstract

We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the $t = 0$ slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.