Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators

TL;DR

This paper models black hole formation holographically through shock wave collisions in AdS3, linking boundary correlators to bulk dynamics and identifying scrambling times via in-time correlators.

Contribution

It introduces a holographic mechanism connecting shock wave collisions to black hole formation and relates scrambling properties to in-time correlators without out-of-time-order analysis.

Findings

Black hole formation occurs after two scrambling times in the dual CFT.

Operator dimensions grow exponentially with boost, dominating the exchanged spectrum.

In-time correlators encode scrambling characteristics typically associated with out-of-time-order correlators.

Abstract

We describe a holographic mechanism for black hole formation via the collision of two shock waves in three-dimensional anti-de Sitter spacetime. In the dual conformal field theory (CFT), a two-shock-wave state corresponds to the insertion of two boosted precursor operators in complementary Rindler patches. Their operator product expansion is initially described by a universal mean-field spectrum of exchanged states, which is dominated by operator dimensions that grow exponentially in the boost parameter. We propose their mean value as diagnosing the mass of the collision product in the bulk. It crosses the CFT heavy state threshold after two scrambling times, in accordance with expectations about black hole formation in general relativity. Our analysis also allows us to identify the scrambling characteristics usually associated with out-of-time-order correlation functions, using only the internal composition of thermal in-time-order correlators.