Pole-skipping and zero temperature

TL;DR

This paper extends pole-skipping analysis to a rotating BTZ background, revealing that pole-skipping frequencies $\omega$ depend on both left- and right-moving temperatures $T_L$ and $T_R$ and the operator dimension. It provides an exact scalar Green's function in terms of products of Gamma functions, identifies the left/right pole and zero structures, and derives explicit pole-skipping conditions from left poles coinciding with right zeros (and vice versa). In the zero-temperature extreme limit, pole-skipping generally vanishes except for special cases (e.g., $\nu=1$) where right-Matsubara frequencies govern the points; the power-series method is shown to fail at extreme horizons, underscoring subtle near-horizon behavior. The results connect to holographic chaos and OTOCs, clarifying how rotation and 2D CFT thermodynamics influence pole-skipping across different regimes.

Abstract

We study the pole-skipping phenomenon of the scalar retarded Green's function in the rotating BTZ black hole background. In the static case, the pole-skipping points are typically located at negative imaginary Matsubara frequencies $ω=-(2πT)ni$ with appropriate values of complex wave number $q$. But, in a $(1+1)$-dimensional CFT, one can introduce temperatures for left-moving and right-moving sectors independently. As a result, the pole-skipping points $ω$ depend both on left and right temperatures in the rotating background. In the extreme limit, the pole-skipping does not occur in general. But in a special case, the pole-skipping does occur even in the extreme limit, and the pole-skipping points are given by right Matsubara frequencies.