Six-point functions and collisions in the black hole interior

Abstract

In the eternal AdS black hole geometry, we consider two signals sent from the boundaries into the black hole interior shared between the two asymptotic regions. We compute three different out-of-time-order six-point functions to quantify various properties of the collision of these signals behind the horizons: (i) We diagnose the strength of the collision by probing the two-signal state on a late time slice with boundary operators. (ii) We quantify two-sided operator growth, which provides a dual description of the signals meeting in the black hole interior, in terms of the quantum butterfly effect and quantum circuits. (iii) We consider an explicit coupling between the left and right CFTs to make the wormhole traversable and extract information about the collision product from behind the horizon. At a technical level, our results rely on the method of eikonal resummation to obtain the relevant gravitational contributions to Lorentzian six-point functions at all orders in the $G_N$-expansion. We observe that such correlation functions display an intriguing factorization property. We corroborate these results with geodesic computations of six-point functions in two- and three-dimensional gravity.

26 pages, 11 figures + 4 appendices; v2: minor improvements

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• Phases of scrambling in eigenstates
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Diagnosing collisions in the interior of a wormhole
• Size and momentum of an infalling particle in the black hole interior
• Collision in the interior of wormhole

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• Shadow Celestial Amplitude
• Seeing behind black hole horizons in SYK
• Quantum gravity of the Heisenberg algebra
• Scattering strings off quantum extremal surfaces
• Collisions of localized shocks and quantum circuits
• Worldsheet traversable wormholes
• Operator growth and black hole formation
• Holographic Black Hole Formation and Scrambling in Time-Ordered Correlators
• Krylov Winding and Emergent Coherence in Operator Growth Dynamics