Chaotic dynamics of string around the conformal black hole

In this paper, we make a systematical and in-depth study on the chaotic dynamics of the string around the conformal black hole. Depending on the characteristic parameter of the conformal black hole and the initial position of the string, there are three kinds of dynamical behaviors: ordered, chaotic and being captured, chaotic but not being captured. A particular interesting observation is that there is a sharp transition in chaotic dynamics when the black hole horizon disappears, which is indepent of the initial position of the string. It provides a possible way to probe the horizon structure of the massive body. We also examine the generalized MSS (Maldacena, Shenker and Stanford) inequality, which is proposed in holographic dual field theory, and find that the generalized MSS inequality holds even in the asymptotically flat black hole background. Especially, as the initial position of the string approaches the black hole horizon, the Lyapunov exponent also approaches the upper bound of the generalized MSS inequality.