Pole-skipping in rotating BTZ black holes

Abstract

A bstract 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 = 2 πiT h ( s − 1 + ν Ω) / (1 − Ω 2 ) 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 $$ {\omega}_{\textrm{leading}}^{\textrm{extremal}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ω</mml:mi> <mml:mtext>leading</mml:mtext> <mml:mtext>extremal</mml:mtext> </mml:msubsup> </mml:math> = −2 πiT 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.

Topics & Concepts