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.
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Shenker, S.H., Stanford, D. Black holes and the butterfly effect. J. High Energ. Phys. 2014, 67 (2014). https://doi.org/10.1007/JHEP03(2014)067
- AdS-CFT Correspondence
- Black Holes