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, ${\lambda }_L^{\pm }=\frac{2\pi }{\beta }\frac{1}{1\mp \ell \Omega }$, where $\Omega$ is the angular velocity and $\ell$ 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 ${\beta }_{\pm }=\beta (1\mp \ell \Omega )$ as the effective inverse temperatures of the left and right moving modes.

35 pages, 2 figures. v2: references added, typos corrected, and clarifications added to the discussion section

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• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Three Dimensional View of the SYK/AdS Duality
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Cited by in corpus (3)

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