Pole-Skipping in Rotating BTZ Black Holes

Hyun-Sik Jeong; Chang-Woo Ji; Keun-Young Kim

doi:10.1007/JHEP08(2023)139

paper

Pole-Skipping in Rotating BTZ Black Holes

arXiv:2306.14805 · doi:10.1007/JHEP08(2023)139

Abstract

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 $ω_{leading} = 2 π i T_{h} (s - 1 + ν Ω) / (1 - Ω^{2})$ where $T_{h}$ is the temperature, $Ω$ the rotation, and $ν := (Δ_{+} - Δ_{-}) /2$ , the difference of conformal dimensions ( $Δ_{\pm}$ ). 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 $ω_{leading}^{extremal} = - 2 π i T_{R} (s + 1)$ only when $ν = s + 1$ , 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 ( $T_{h} \to 0, Ω \to 1$ ) of the non-extremal black hole result.

arXiv comment41 pages

Pole-Skipping in Rotating BTZ Black Holes

Abstract

References in corpus (37)

Cited by in corpus (10)