Seeing behind black hole horizons in SYK

TL;DR

This paper demonstrates how to reconstruct the interior of an AdS$_2$ black hole within the dual SYK model without direct bulk reference, using a probe observer and SYK operators transported along its infalling trajectory.

Contribution

It introduces a method to explicitly reconstruct black hole interiors in SYK purely from boundary data, extending the understanding of holographic duality and interior geometry.

Findings

Successfully recovers the proper time for signals inside the wormhole.

Utilizes universal properties of SYK for interior reconstruction.

Outlines potential extensions to higher dimensions and scattering amplitudes.

Abstract

We present an explicit reconstruction of the interior of an AdS$_2$ black hole in Jackiw-Teitelboim gravity, that is entirely formulated in the dual SYK model and makes no direct reference to the gravitational bulk. We do this by introducing a probe "observer" in the right wormhole exterior and using the prescription of [arXiv:2009.04476] to transport SYK operators along the probe's infalling worldline and into the black hole interior, using an appropriate SYK modular Hamiltonian. Our SYK computation recovers the precise proper time at which signals sent from the left boundary are registered by our observer's apparatus inside the wormhole. The success of the computation relies on the universal properties of SYK and we outline a promising avenue for extending it to higher dimensions and applying it to the computation of scattering amplitudes behind the horizon.