The aim of this note is to explore Susskind's proposal [1] on the connection between operator size in chaotic theories and the bulk momentum of a particle falling into black holes (see also [2], [3], [4], [5], [6] for more recent generalizations), in a broad class of models involving Gauss-Bonnet(GB) and Lifshitz-Hyperscaling violating theories in AdS. For Gauss-Bonnet black holes, the operator size is seen to be suppressed as the coupling constant λ is increased. For the Lifshitz-hyperscaling violating theories characterised by the parameters z and θ, the operator size is higher as compared to case $z=1,\theta =0$ (Reissner-Nordstrom AdS black holes). In the case of operators with global charge corresponding to charged particles falling into black holes, suppression of chaos is seen in general theories of gravity, in conformity with the original proposal [1] and earlier findings [3].

本笔记的目的是探讨 Susskind 关于混沌理论中算子大小与落入黑洞的粒子的体积动量之间的联系的提议 [1]（另见 [2]、[3]、[4]、[5] ], [6] 用于最近的概括），在涉及高斯-博内（GB）和 Lifshitz-Hyperscaling 违反 AdS 理论的一大类模型中。对于 Gauss-Bonnet 黑洞，随着耦合常数λ的增加，算子大小被抑制。对于以参数z和θ 为特征的 Lifshitz 超标度违反理论，与 case 相比，算子大小更高$z=1,\theta =0$（Reissner-Nordstrom AdS 黑洞）。在具有对应于落入黑洞的带电粒子的全局电荷的算子的情况下，在一般引力理论中可以看到对混沌的抑制，这与最初的提议 [1] 和早期的发现 [3] 一致。