Six-point functions and collisions in the black hole interior

TL;DR

This paper analyzes six-point functions in the context of eternal AdS black holes to understand signal collisions behind horizons, operator growth, and traversability, using eikonal resummation and geodesic computations.

Contribution

It introduces a method to compute out-of-time-order six-point functions in black hole interiors, revealing factorization properties and insights into traversability and operator growth.

Findings

Six-point functions reveal collision strength behind horizons.

Operator growth relates to quantum butterfly effect.

Traversable wormholes allow extraction of collision information.

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.