浸没在 quintessence 暗能量中的 Rastall 旋转黑洞中的重复彭罗斯过程
Repetitive Penrose Process in Rastall Rotating Black Holes Immersed in Quintessence Dark Energy
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中文总结 AI 辅助
研究浸没在 quintessence 暗能量中的 Rastall 旋转黑洞的重复彭罗斯过程，通过推导守恒及迭代方程制定该过程，确定终止条件与临界停止标准，发现粒子 0 控制过程，且无量纲 Rastall 结构参数和耦合参数显著影响能量提取。
中文摘要 AI 辅助
我们研究了被 quintessence 暗能量场包围的 Rastall 旋转黑洞时空中的重复彭罗斯过程。在回顾黑洞几何的基本性质后，通过推导能层内粒子分裂的守恒方程以及相应的迭代演化方程来制定重复彭罗斯过程。确定了终止能量提取迭代所需的物理条件，并分析了衰变粒子的最小自旋阈值以确定临界停止标准。分析表明，重复彭罗斯过程的终止始终由粒子 0 控制，它在所有衰变产物中具有最高的最小自旋阈值。数值结果进一步表明，无量纲 Rastall 结构参数 $\hat{N}_s$ 和 Rastall 耦合参数 $\alpha$ 对能量提取过程的演化有显著影响。在相同的衰变半径下，这两个参数的初始值增加会提高能量利用效率和能量投资回报率。具体而言，较小的 $\hat{N}_s$ 值在较低衰变半径下提高能量利用效率，将最大提取能量向较低衰变半径移动，并加速剩余可提取能量储备的消耗。这表明重复彭罗斯过程在较低衰变半径下非常有利。较小的 $\hat{N}_s$ 初始值产生更大的最大能量投资回报率。同样，增加 $\alpha$ 会提高能量利用效率，改变峰值提取能量的位置，并减少总可提取能量。但与 $\hat{N}_s$ 相比，$\alpha$ 对这些能量学的影响非常小。
英文摘要
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 $α$ 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 $α$ enhances the energy utilization efficiency, alters the location of the peak extracted energy, and reduces the total extractable energy. But the effects of $α$ on these energetics are very small as compared to $\hat{N}_s$.
