Butterflies on the Stretched Horizon

Abstract

In this paper I return to the question of what kind of perturbations on Alice's side of an Einstein-Rosen bridge can send messages to Bob as he enters the horizon at the other end. By definition "easy" operators do not activate messages and "hard" operators do, but there are no clear criteria to identify the difference between easy and hard. In this paper I argue that the difference is related to the time evolution of a certain measure of computational complexity, associated with the stretched horizon of Alice's black hole. The arguments suggest that the AMPSS commutator argument is more connected with butterflies than with firewalls.

Additional citations and substantive additions. All additions indicated in boldface

References in corpus (4)

• Black holes as mirrors: quantum information in random subsystems
• State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
• The Black Hole Interior in AdS/CFT and the Information Paradox
• New Concepts for Old Black Holes

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• New Concepts for Old Black Holes
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• Computational Complexity and Black Hole Horizons
• Cold Black Holes in the Harlow-Hayden Approach to Firewalls
• Black Holes, Entropies, and Semiclassical Spacetime in Quantum Gravity
• Charge Loss (or the Lack Thereof) for AdS Black Holes
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• Complexity Near Horizons
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• Complexity growth rate, grand potential and partition function