Effects of the acceleration on holographic complexity

In this work, we consider a special kind of space{time called AdS accelerating black holes. This is a kind of black holes which have a stringlike singularity along polar axis attached to the black hole and it accelerates the black hole. In these kind of space{times, the growth of Einstein{Hilbert action is independent of the acceleration as found in S. Chen and Y. Pei, Int. J. Theor. Phys. 60, 917 (2021). By using a string as a probe, we found the effect of the acceleration is captured by the string probe [K. Nagasaki, arXiv:2108.05429 [hep-th]]. Here in this work, we consider the case of rotating black holes. By the probe string, we clearly describe the effect of the acceleration and its relation to the rotation of the black holes.