Chaotic Fast Scrambling At Black Holes

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.