We study the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. For describing hyperscaling violating system, we chose a particular gravity model constructed from generalized Einstein-Maxwell-Dilaton action which includes the Lifshitz cases at appropriate limits. We study the relationship between Lyapunov exponents and black hole phase transitions considering both the timelike and null geodesics. We observe that, the black hole phase transiton properties are reflected in Lyapunov exponent where its multiple branches correspond to the distinct phases of the black hole. The discontinuos change of the Lyapunov exponent during the phase transition serve as an order parameter with critical exponent 1/2 near the critical point. Our numerical study reveals that the correlation between the Lyapunov exponent and black hole thermodynamic properties can be generalised beyond the AdS spacetime. We find that it is independent of the HSV parameter as well as the Lifshitz exponent.

中文翻译：

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Lifshitz 和超尺度破坏黑洞的 Lyapunov 指数和相结构


我们使用 Lyapunov 指数研究 Lifshitz 和超尺度破坏 (HSV) 黑洞的相结构。为了描述超尺度破坏系统，我们选择了一个由广义爱因斯坦-麦克斯韦-膨胀作用构建的特定重力模型，其中包括适当限制的 Lifshitz 情况。我们研究了李雅普诺夫指数与黑洞相变之间的关系，同时考虑了类时测地线和零测地线。我们观察到，黑洞相变特性反映在李亚普诺夫指数中，其中它的多个分支对应于黑洞的不同相位。相变过程中李亚普诺夫指数的不连续变化作为阶次参数，临界点附近的临界指数为1/2。我们的数值研究表明，李亚普诺夫指数和黑洞热力学性质之间的相关性可以推广到 AdS 时空之外。我们发现它与 HSV 参数以及 Lifshitz 指数无关。