Construction of bulk solutions for towers of pole-skipping points

TL;DR

This paper analyzes the pole-skipping phenomenon in black hole geometries, constructing solutions for integer spin fields and exploring towers of special points related to chaotic properties and four-point amplitudes.

Contribution

It introduces a method to construct solutions for higher-spin fields at pole-skipping points and proposes horizon integrals of propagators as a way to understand these phenomena.

Findings

Identified towers of pole-skipping points for integer spin fields.

Linked horizon integrals of bulk propagators to behaviors at special points.

Provided a new interpretation in terms of four-point amplitudes with spin exchange.

Abstract

The pole-skipping phenomenon has been proposed as a connection between chaotic properties of black hole geometries and special points where regular solutions of linearized Einstein equations at horizons have extra free parameters. In this work, we pursue the special points in the near-horizon analysis of integer spin-$\ell$ fields on the Rindler-AdS black hole. We construct linear combinations of field components to simplify coupled equations of massive fields and investigate towers of the special points along with imaginary Matsubara frequencies $i\omega=2\pi(n+1-\ell)T$ with a non-negative integer $n$ and the Hawking temperature $T$. We also propose that integrals of spin-$\ell$ bulk propagators over horizons of static black holes capture behaviors at the special points, which are generalizations of integrals of graviton propagators for shock wave geometries. Their interpretation is provided in terms of four-point amplitudes with the spin-$\ell$ exchange.