Pole-Skipping in Rotating BTZ Black Holes

• Published in: arXiv.org 2023-06
• Main Authors: Jeong, Hyun-Sik, Chang-Woo, Ji, Keun-Young, Kim
• Format: Article
• Language: English
• Subjects: Green's functions; Rotation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2306.14805

Motivated by the connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating BTZ black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin \(s = 1/2, 1, 2/3\), extending the previous research for \(s=0, 2\). We derive an analytic full tower of the pole-skipping points of fermionic (\(s=1/2\)) and vector (\(s=1\)) fields by the exact holographic Green's functions. For the \textit{non-extremal} black hole, the leading pole-skipping frequency is \(\omega_{\text{leading}}=2\pi i T_h {(s-1+\nu \Omega)}/{(1-\Omega^2)}\) where \(T_h\) is the temperature, \(\Omega\) the rotation, and \(\nu:=(\Delta_+ - \Delta_-)/2\), the difference of conformal dimensions (\(\Delta_{\pm}\)). These are confirmed by another independent method: the near-horizon analysis. For the \textit{extremal} black hole, we find that the leading pole-skipping frequency can occur at \(\omega_{\text{leading}}^{\text{extremal}}=-2\pi i T_R {(s+1)}\) only when \(\nu = s+1\), where \(T_R\) is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit (\(T_h\rightarrow 0\,, \Omega\rightarrow 1\)) of the non-extremal black hole result.