Continuing past the inner horizon using WKB

TL;DR

This paper develops analytic continuation methods in boundary correlation functions to probe the interior of rotating and charged black holes, revealing contributions from timelike geodesics and non-perturbative effects in the WKB approximation.

Contribution

It introduces new analytic continuation techniques in momentum and position space to access black hole interiors, including non-perturbative corrections to the WKB approximation.

Findings

Geodesic contributions from the interior are captured in continued correlators.

Analytic continuations reveal non-perturbative effects in black hole interior probes.

The methods are exemplified in rotating BTZ and AdS Schwarzschild black holes.

Abstract

Features of the black hole interior can be extracted from the analytic structure of boundary correlation functions. Working in the geodesic approximation, we find analytic continuations that probe the interior of rotating and charged black holes. These generate contributions from timelike geodesics that thread the interior and emerge in a future universe. We implement these continuations on the momentum space two-point function and exemplify this in several black hole backgrounds. We also identify position space analytic continuations achieving the same task that incorporate different continued momentum space correlators. These correspond to non-perturbative corrections to the WKB approximation. We demonstrate this explicitly in the rotating BTZ black hole by showing that the interior geodesics contribute to the continued position space correlator and motivate a picture for how these contributions arise in higher dimensions. For AdS Schwarzschild, we identify the analytically continued solution that captures the bouncing geodesic. We discuss the possibility of using these continuations to probe the instability of inner horizons from the boundary.