Fast Scramblers And Ultrametric Black Hole Horizons

TL;DR

This paper models fast information scrambling on black hole horizons using ultrametric diffusion, revealing a logarithmic scrambling time and instability at infinite entropy, with connections to Kohlrausch law.

Contribution

It introduces a novel ultrametric diffusion model for black hole horizon scrambling, linking causality bounds to logarithmic scrambling times.

Findings

Scrambling time scales logarithmically with entropy.

Ultrametric diffusion becomes unstable at infinite entropy.

Regularized model follows Kohlrausch law.

Abstract

We propose that fast scrambling on finite-entropy stretched horizons can be modeled by a diffusion process on an effective ultrametric geometry. A scrambling time scaling logarithmically with the entropy is obtained when the elementary transition rates saturate causality bounds on the stretched horizon. The so-defined ultrametric diffusion becomes unstable in the infinite-entropy limit. A formally regularized version can be shown to follow a particular case of the Kohlrausch law.