Holographic chaos, pole-skipping, and regularity

TL;DR

The paper investigates pole-skipping in holographic chaos by examining the regularity of near-horizon perturbations. Using gauge-invariant variables and curvature invariants in Schwarzschild–AdS$_4$, it shows that at the special point both horizon solutions are regular and the incoming boundary condition is not uniquely defined, due to slope dependence as one approaches the point. It further demonstrates that, away from the special point, one solution is generically singular in the upper-half ω-plane, while at the special point this singular behavior disappears. The results provide a robust framework for understanding pole-skipping through horizon regularity, with implications for interpreting 2-point functions as probes of chaotic dynamics in holographic systems.

Abstract

We investigate the "pole-skipping" phenomenon in holographic chaos. According to the pole-skipping, the energy-density Green's function is not unique at a special point in complex momentum plane. This arises because the bulk field equation has two regular near-horizon solutions at the special point. We study the regularity of two solutions more carefully using curvature invariants. In the upper-half $ω$-plane, one solution, which is normally interpreted as the outgoing mode, is in general singular at the future horizon and produces a curvature singularity. However, at the special point, both solutions are indeed regular. Moreover, the incoming mode cannot be uniquely defined at the special point due to these solutions.