Repetitive Penrose Process in Rastall Rotating Black Holes Immersed in Quintessence Dark Energy

Abstract

We investigate the repetitive Penrose process in the spacetime of a Rastall rotating black hole surrounded by a quintessence dark energy field. After reviewing the fundamental properties of the black hole geometry, we formulate the repetitive Penrose process by deriving the conservation equations governing particle splitting within the ergoregion, along with the corresponding iterative evolution equations. The physical conditions required for terminating the energy extraction iterations are established, and the minimum spin thresholds of the decay particles are analyzed to identify the critical stopping criterion. Our analysis reveals that the termination of the repetitive Penrose process is consistently governed by Particle~$0$, which possesses the highest minimum spin threshold among all decay products. Numerical results further demonstrate that the dimensionless Rastall structure parameter $\hat{N}_s$ and the Rastall coupling parameter $\alpha$ significantly influence the evolution of the energy extraction process. At the same decay radii increasing initial values of both parameters boosts the energy utilization efficiency and energy return on investment. Specifically, smaller values of $\hat{N}_s$ enhances the energy utilization efficiency at lower decay radii, shifts the maximum extracted energy toward lower decay radii, and accelerates the depletion of the remaining extractable energy reservoir. This indicates that the repetitive Penrose process is highly favored at lower decay radii. Smaller initial values of $\hat{N}_s$ yield a larger maximum energy return on investment. Similarly, increasing $\alpha$ enhances the energy utilization efficiency, alters the location of the peak extracted energy, and reduces the total extractable energy. But the effects of $\alpha$ on these energetics are very small as compared to $\hat{N}_s$.