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

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.