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, \( {\lambda}_L^{\pm }=\frac{2\pi }{\beta}\frac{1}{1\mp \ell \Omega} \), where Ω is the angular velocity and ℓ is the AdS radius. Since \( {\lambda}_L^{-}\le \frac{2\pi }{\beta}\le {\lambda}_L^{+} \), 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.
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Jahnke, V., Kim, KY. & Yoon, J. On the chaos bound in rotating black holes. J. High Energ. Phys. 2019, 37 (2019). https://doi.org/10.1007/JHEP05(2019)037
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DOI: https://doi.org/10.1007/JHEP05(2019)037