On the chaos bound in rotating black holes

Abstract

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 ± = 2 π β 1 1 ∓ ℓ Ω $$ {\lambda}_L^{\pm }=\frac{2\pi }{\beta}\frac{1}{1\mp \ell \Omega} $$ , where Ω is the angular velocity and ℓ is the AdS radius. Since λ L − ≤ 2 π β ≤ λ L + $$ {\lambda}_L^{-}\le \frac{2\pi }{\beta}\le {\lambda}_L^{+} $$ , 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 ∓ ℓΩ) as the effective inverse temperatures of the left and right moving modes.

Keywords

• AdS-CFT Correspondence
• Gauge-gravity correspondence