Pole skipping in a non-black-hole geometry
Makoto Natsuume, Takashi Okamura
Abstract
Pole skipping has been discussed in black-hole backgrounds, but we point out that pole skipping exists even in a non-black-hole background, the anti--de Sitter soliton. For black holes, the pole-skipping points are typically located at imaginary Matsubara frequencies $\ensuremath{\omega}=\ensuremath{-}(2\ensuremath{\pi}T)ni$ with an integer $n$. The anti--de Sitter soliton is obtained by the double Wick rotation from a black hole. As a result, the pole-skipping points are located at ${q}_{z}=\ensuremath{-}(2\ensuremath{\pi}n)/l$, where $l$ is the ${S}^{1}$ periodicity and ${q}_{z}$ is the ${S}^{1}$ momentum. The ``chaotic'' and the ``hydrodynamic'' pole-skipping points lie in the physical region. We also propose a method to identify all pole-skipping points instead of the conventional method.