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Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators

School of Physics and Astronomy and STAG Research Centre, University of Southampton, SO17 1BJ, Southampton, United Kingdom

School of Mathematical Sciences and STAG Research Centre, University of Southampton, SO17 1BJ, Southampton, United Kingdom

MIT Center for Theoretical Physics—a Leinweber Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Phys. Rev. Lett. 136, 121601 – Published 23 March, 2026

DOI: https://doi.org/10.1103/ywfb-82lh

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, 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 conformal field theory 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.

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Phys. Rev. Lett. 136, 121601– Published 23 March, 2026

Vol. 136, Iss. 12 — 27 March 2026

Received 24 November 2025
Accepted 12 February 2026

DOI: https://doi.org/10.1103/ywfb-82lh

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators

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