On the chaos bound in rotating black holes

Abstract

We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes using two di ff erent approaches: the elastic eikonal gravity approximation, and the ChernSimons 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 di ff erent Lyapunov exponents, L = 2 fi 1 1`, where is the angular velocity and ` is the AdS radius. Since 2 fi + 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 fi = fi (1 ` ) as the e ff ective inverse temperatures of the left and right moving modes.