On the Chaos Bound in Rotating Black Holes

Abstract

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, $λ_L^{\pm}=\frac{2π}β\frac{1}{1\mp \ell Ω}$, where $Ω$ is the angular velocity and $\ell$ is the AdS radius. Since $λ_L^{-} \leq \frac{2π}β \leq λ_L^{+}$, 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 $β_{\pm}=β(1\mp \ell Ω)$ as the effective inverse temperatures of the left and right moving modes.