Chaotic Fast Scrambling At Black Holes
Jose L. F. Barbon, Javier M. Magan

TL;DR
This paper explores the rapid information scrambling in black holes using the AdS/CFT correspondence, proposing a hyperbolic billiard model to explain classical chaos as a key factor in fast scrambling.
Contribution
It introduces a geometrical interpretation of causality bounds via optical depth and models scrambling as a hyperbolic billiard, linking chaos to black hole information dynamics.
Findings
Causality bounds depend on the optical depth of the Rindler region.
Scrambling can be modeled as a hyperbolic billiard exhibiting classical chaos.
Classical chaos at large N is crucial for fast scrambling and causality saturation.
Abstract
Fast scramblers process information in characteristic times scaling logarithmically with the entropy, a behavior which has been conjectured for black hole horizons. In this note we use the AdS/CFT fold to argue that causality bounds on information flow only depend on the properties of a single thermal cell, and admit a geometrical interpretation in terms of the optical depth, i.e. the thickness of the Rindler region in the so-called optical metric. The spatial sections of the optical metric are well approximated by constant-curvature hyperboloids. We use this fact to propose an effective kinetic model of scrambling which can be assimilated to a compact hyperbolic billiard, furnishing a classic example of hard chaos. It is suggested that classical chaos at large N is a crucial ingredient in reconciling the notion of fast scrambling with the required saturation of causality.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
