# Holographic chaos, pole-skipping, and regularity

## TL;DR

This paper explores the pole-skipping phenomenon in holographic chaos, revealing how regularity conditions at special points in the complex momentum plane affect the uniqueness of Green's functions and the interpretation of modes.

## Contribution

It provides a detailed analysis of the regularity of solutions at pole-skipping points, clarifying the nature of incoming and outgoing modes in holographic chaos.

## Key findings

- Both solutions are regular at the special pole-skipping point.
- The incoming mode cannot be uniquely defined at the special point.
- Curvature invariants reveal singularities are absent at the pole-skipping point.

## 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 $\omega$-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.