Pole-skipping in rotating BTZ black holes

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 non-extremal black hole, the leading pole-skipping frequency is ω_leading = 2πiT_h(s − 1 + νΩ)/(1 − Ω²) where T_h is the temperature, Ω the rotation, and ν := (∆₊ − ∆₋)/2, the difference of conformal dimensions (∆_±). These are confirmed by another independent method: the near-horizon analysis. For the extremal black hole, we find that the leading pole-skipping frequency can occur at ${\omega }_{\text{leading}}^{\text{extremal}}$ = −2πiT_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 → 0, Ω → 1) of the non-extremal black hole result.