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This paper studies the quasinormal mode spectrum of the scalar perturbation on the background of the rotating accelerating black holes. The quasinormal frequency and the separation constant are calculated using two methods: the continued fractions method and the direct integration method. The spectrum is found to include three families of modes: the photon sphere modes, the acceleration modes, and the near extreme modes. We investigate the effects of back hole parameters such as spin and acceleration. Empirical formulas are presented for the numerical results, specifically for the acceleration modes in the small black hole limit or the near extreme modes in the extreme black hole limit. An interesting phenomenon known as eigenvalue repulsion is observed when the acceleration modes intersect with the near extreme modes at certain parameter values. The strong cosmic censorship conjecture for spinning C-metric is respected.
Xiong et al. (Mon,) studied this question.