标题： 洛伦兹黑洞的广义体积-复杂度 显示英文标题

标题： Generalized volume-complexity for Lovelock black holes

摘要： 在本研究中，我们通过“复杂性=任何事物”假说探讨了Lovelock黑洞的广义复杂性的时间依赖性，该假说扩展了“复杂性=体积”的概念，并生成了一大类可观测量。 通过应用特定条件，可以选择一个更有限的类别，其时间增长等同于一个守恒动量。 具体而言，我们研究了复杂性时间率的数值全时间行为，重点关注Lovelock理论的二阶和三阶，将背景时空的Weyl张量的平方作为附加项纳入泛化函数中。 此外，我们研究了三种附加标量项的情况：Riemann张量和Ricci张量的平方以及二阶引力（GB）中的Ricci标量，并展示了它如何影响时间的多种渐进行为。 此外，我们展示了广义复杂性的相变及其在$\tau_{turning}$点的时间演化，此时最大广义体积取代了另一个分支。 此外，我们展示了在晚期时间，复杂性时间率与两个视界温度乘以熵的差值（$TS(r_+)-TS(r_-)$）成正比，这在广义情况下可以通过每个半径的函数进行修正。 显示英文摘要

摘要： In this study, We explore the time dependence of the generalized complexity of Lovelock black holes via the "complexity = anything" conjecture, which expands upon the notion of "complexity = volume" and generates a large class of observables. By applying a specific condition, a more limited class can be chosen, whose time growth is equivalent to a conserved momentum. Specifically, we investigate the numerical full time behavior of complexity time rate, focusing on the second and third orders of Lovelock theory, incorporating an additional term -- the square of the Weyl tensor of the background spacetime -- into the generalization function. Furthermore, we study the case with three additional scalar terms: the square of Riemann and Ricci tensors, and the Ricci scalar for second-order gravity (GB) and show how it can affect to multiple asymptotic behavior of time. Additionally, we show how the phase transition of generalized complexity and its time evolution occur at $\tau_{turning}$ point where the maximal generalized volume supersedes another branch. Moreover, we show the proportionality complexity time rate at late times to the difference of temperature times entropy in two horizons ($TS(r_+)-TS(r_-)$) for charged black holes, which can be corrected by a function of each radius in generalized case.