We consider the growth of the action for black hole space–time with a fundamental string. Our interest is to find the difference of the behavior between black holes with three different topologies in the scenario of complexity-action conjecture. These black holes have positive, negative and zero curvatures. We would like to calculate the action growth of these systems with a probe fundamental string according to the complexity-action conjecture. We find that for the case where the black holes have the toroidal horizon structure this probe string behaves very differently from the other two cases.

中文翻译：

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拓扑黑洞的全息法复杂度增长

我们用一个基本弦来考虑黑洞时空作用的增长。我们的兴趣是在复杂性-作用猜想的场景中找到具有三种不同拓扑的黑洞之间的行为差​​异。这些黑洞有正曲率、负曲率和零曲率。我们想根据复杂性-动作猜想，用一个探测基本弦来计算这些系统的动作增长。我们发现，对于黑洞具有环形视界结构的情况，该探测弦的行为与其他两种情况非常不同。