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： 我们使用“复杂性=任何事物”假说研究洛塞尔克黑洞的广义复杂性的时变特性，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，其时间增长等价于守恒动量。 具体而言，我们研究了复杂性时间率的数值全时行为，重点研究了与麦克斯韦项耦合的洛塞尔克理论的二阶和三阶情况，并在泛化函数中引入了一个额外项——背景时空的Weyl张量的平方。 此外，我们对包含三个额外标量项的情况进行了分析：Riemann张量和Ricci张量的平方，以及二阶引力（Gauss-Bonnet）中的Ricci标量，展示了这些项如何影响时间的多种渐近行为。 我们研究了广义复杂性的相变及其在转折点$(\tau_{turning})$处的时间演化，此时最大广义体积取代了另一分支。 此外，我们讨论了晚期时间行为，重点关注带电黑洞的复杂性时间率与两个视界处温度乘以熵的差值的成比例关系（$TS(r_+)-TS(r_-)$），这可以在广义情况下通过每个半径的泛化函数进行修正。 在这个极限下，我们还通过将时空近似为Kasner度规来探索接近奇点的结构，并通过不同选择的泛化函数找到可能的复杂性增长速率。 显示英文摘要

摘要： We study the time dependence of the generalized complexity of Lovelock black holes using 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 coupled with Maxwell term, incorporating an additional term -- the square of the Weyl tensor of the background spacetime -- into the generalization function. Furthermore, we repeat the analysis for case with three additional scalar terms: the square of Riemann and Ricci tensors, and the Ricci scalar for second-order gravity (Gauss-Bonnet) showing how these terms can affect to multiple asymptotic behavior of time. We study how the phase transition of generalized complexity and its time evolution occur at turning point $(\tau_{turning})$ where the maximal generalized volume supersedes another branch. Additionally, we discuss the late time behavior, focusing on proportionality of the complexity time rate to the difference of temperature times entropy at the two horizons ($TS(r_+)-TS(r_-)$) for charged black holes, which can be corrected by generalization function of each radius in generalized case. In this limit, we also explore near singularity structure by approximating spacetime to Kasner metrics and finding possible values of complexity growth rate with different choices of the generalization function.