Pole skipping and zero temperature
Makoto Natsuume, Takashi Okamura
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 $\ensuremath{\omega}=\ensuremath{-}(2\ensuremath{\pi}T)ni$ 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 $\ensuremath{\omega}$ 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.