In this work, we present the effect of a probe string on the complexity of a black hole according to the CA (Complexity equals action) conjecture on Horndeski’s gravity. In our system, we consider a particle moving on the boundary of black hole spacetime in (\(2+1\))-dimensions. To obtain a dual description, we need to insertion a fundamental string on the bulk spacetime. The effect of this string is given by the Nambu–Goto term. For the Nambu–Goto term, we can analyze the time development of this system, which is affected by the parameters of Horndeski’s gravity. In our case, we show some interesting complexity properties for this gravity.

在这项工作中，我们根据Horndeski引力的CA（复杂度等于作用）猜想，展示了探针串对黑洞复杂度的影响。在我们的系统中，我们考虑以（\（2 + 1 \））维在黑洞时空边界上移动的粒子。为了获得双重说明，我们需要在批量时空上插入一个基本字符串。该字符串的效果由Nambu–Goto术语给出。对于Nambu–Goto项，我们可以分析该系统的时间发展，这受Horndeski引力参数的影响。在我们的案例中，我们展示了此引力的一些有趣的复杂性属性。