Repetitive Penrose Process in Accelerating Kerr Black Holes

This paper investigates the repetitive Penrose process in accelerating Kerr black holes and explores the influence of the acceleration factor on the repetitive Penrose process. After a brief review of accelerating Kerr black holes, we study the fundamental equations of the Penrose process in this spacetime, examine the stopping conditions required for the repetitive Penrose process, and obtain corresponding numerical results. The conclusions indicate that, apart from the third law of thermodynamics similar to previous cases, accelerating Kerr black holes exhibit stronger energy extraction capabilities compared to Kerr black holes during the repetitive Penrose process. Moreover, in prior studies, the energy utilization efficiency was difficult to exceed $50\%$. However, in accelerating Kerr black holes, when the decay radius is relatively small, the energy utilization efficiency can exceed $50\%$, indicating that the reduced extractable energy primarily transforms into extracted energy rather than irreducible mass. On the other hand, when the initial value of the acceleration factor is large, the extractable energy can decrease to nearly zero, which also differs from the case of Kerr black holes in previous studies.