arXiv 1908.093102019-08hep-th

Lovelock黑洞复杂性的时间依赖性

Time dependence of complexity for Lovelock black holes

Zhong-Ying Fan, Hua-Zhi Liang

备注：: 10.1103/PhysRevD.100.086016; minor revisions, references added,43pages,13figures
发表信息：: Phys. Rev. D 100, 086016 (2019)
DOI：: 10.1103/PhysRevD.100.086016

摘要：

本文采用“复杂性=作用”（CA）的方法研究了与Lovelock黑洞对偶的全息态的复杂性对时间的一般依赖性。我们观察到，在早期，复杂性开始增加的临界时间是高阶耦合常数的递减函数，这意味着复杂性的演化速度比Schwarzschild黑洞。在后期，复杂性的变化率基本上是由广义Gibbons-Hawking-York边界项在未来奇点处的评估决定的。特别是，它与黑洞质量的比值是一个特征常数，与高阶耦合无关。因此，在耦合极限为零的情况下，尽管度规和引力作用都归约为史瓦西黑洞的结果，但结果一般不会归约为史瓦西黑洞的结果。事实上，在整个时间演化过程中，两者相差一个常数。包括次到领先的顺序项附近晚的时间，我们发现，作为爱因斯坦的情况下，晚的时间限制总是接近从上面，从而违反任何限制的上限所给出的晚的时间的结果。对于荷电Lovelock黑洞，我们发现，有足够的电荷，复杂性的行为大致相同的爱因斯坦的情况。但是，对于较小的费用，两者有一些明显的差异。特别是，不同于爱因斯坦的情况下，在不带电的限制的复杂性增长率不匹配的中性的情况下，不同的常数在整个时间的演变。

英文摘要：

We study the general time dependence of complexity for holographic states dual to Lovelock black holes using the "Complexity=Action" (CA) proposal. We observe that at early times, the critical time at which the complexity begins to increase is a decreasing function of the higher order coupling constants, which implies that the complexity evolves faster than that of Schwarzschild black holes. At late times, the rate of change of complexity is essentially determined by the generalised Gibbons-Hawking-York boundary term evaluated at the future singularity. In particular, its ratio to black hole mass is a characteristic constant, independent of the higher order couplings. Thus, in the vanishing coupling limit, the result in general does not reduce to that of Schwarzschild black holes, in spite of that the metric reduces to the latter as well as the gravitational action. In fact, the two differ by a constant during the whole time evolution. Including the next-to-leading order term around late times, we find that as the Einstein case, the late time limit is always approached from above, thus violating any conjectured upper bound given by the late time result. For charged Lovelock black holes, we find that with sufficient charge, the complexity roughly behaves the same as the Einstein case. However, for smaller charges, the two have some significant differences. In particular, unlike the Einstein case, in the uncharged limit the complexity growth rate does not match with the neutral case, differing by a constant in the whole time evolution.

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