Imprint of the black hole interior on thermal four-point correlators

TL;DR

This paper develops a method to analyze thermal four-point correlators in AdS black holes, revealing how interior black hole physics influences boundary measurements through a novel dictionary and factorization into flat-space scattering amplitudes.

Contribution

It introduces a new dictionary linking boundary smeared operators to interior flat-space oscillators, enabling the study of black hole interior physics via boundary correlators.

Findings

Correlators factorize into flat-space scattering amplitudes near the interior.

The method captures local interior physics with exponential suppression.

Operator time ordering is crucial for accessing interior information.

Abstract

We consider correlators smeared against directed wavepackets over a thermal state dual to a single-sided planar AdS black hole. In the large frequency limit, our measurement is simplified using a bulk WKB description. We propose a dictionary that maps the action of smeared boundary operators to flat-space oscillators near an interior bulk point on the thermal state, by analytically continuing late-time operators from the right to the left boundary via an integral transform. Using the dictionary the smeared correlator factorizes to a flat-space like scattering amplitude about the interior event. Our transformed correlators describe local physics in the two-sided black hole interior, while incurring a suppression of $\mathcal{O}(e^{-\beta \omega / 2})$. These measurements necessitate a non-trivial time ordering of operators living on boundary hyperboloids which are causally connected to the past light cone of the bulk point, as well as on a corresponding future branch.