On the chaos bound in rotating black holes

A bstract We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes using two different approaches: the elastic eikonal gravity approximation, and the Chern-Simons formulations of 3-dimensional gravity. Within both methods the OTOC is given as a sum of two contributions, corresponding to left and right moving modes. The contributions have different Lyapunov exponents, λL±=2π /β1/1∓ Ω λ L ± = 2 π β 1 1 ∓ ℓ Ω , where Ω is the angular velocity and ℓ is the AdS radius. Since λL⁻≤ 2π /β≤ λL⁺ λ L − ≤ 2 π β ≤ λ L + , there is an apparent contradiction with the chaos bound. We discuss how the result can be made consistent with the chaos bound if one views the parameters β ± = β (1 ∓ ℓ Ω) as the effective inverse temperatures of the left and right moving modes.