Repetitive Penrose process for charged particles in Kerr-Newman black holes

Abstract: We investigate the repetitive Penrose process for charged particles in an initially extremal Kerr--Newman black hole and develop a nonlinear iterative framework in which the black-hole mass, angular momentum, electric charge, and irreducible mass are updated after every extraction event. By imposing the triple turning-point condition, we obtain an analytic solution of the conservation equations, allowing the entire extraction sequence to be followed self-consistently. The dynamics are governed by two electromagnetic couplings. The coupling $\hat Q\hat q_0$ determines whether the incident particle can continue to access the ergoregion and therefore controls the termination of the repetitive process, whereas $\hat Q\hat q_1$ governs the depth of the negative-energy states and the extraction efficiency. An attractive interaction ($\hat Q\hat q_1<0$) significantly enhances both the energy return on investment and the energy utilization efficiency and, above a critical charge, produces a transient increase of the dimensionless spin despite the continuous loss of angular momentum. We identify a four-region structure in the captured-particle charge parameter space. Near the critical charge $\hat q_1\simeq-54.85405$, the evolution approaches the reversible Christodoulou--Ruffini limit with the energy utilization efficiency approaching unity while the black hole remains sub-extremal. Beyond this point the irreducible mass decreases, indicating the breakdown of the test-particle approximation. Unlike the repetitive Penrose process in the extremal Reissner--Nordström spacetime, the Kerr--Newman black hole can evolve through the neutral state and reverse the sign of its electric charge without violating the area theorem or cosmic censorship, demonstrating that the discharge barrier found in the Reissner--Nordström case is not a generic property of charged black holes.