Repetitive Magnetic Penrose Process

Abstract

The nonlinear iterative repetitive Penrose process established recently by Ruffini et al.\ is generalized to the magnetic Penrose process. The spacetime background is the Kerr metric, the external magnetic field is described by the Wald solution, the electromagnetic field is treated as a test field, and the charge is treated as a test charge. We analyze the optimal conditions for maximum energy extraction on the equatorial plane and find that under these conditions the core mechanism of the iterative process is charging feedback. After charging, the black hole charge is approximately half of the Wald charge. When the neutral parent particle decays, charge conservation forces the infalling fragment to carry charge while the other fragment carries the opposite charge, so the black hole charge accumulates monotonically. The monopole voltage of the Wald solution decreases linearly with the charge $Q$ and crosses zero to reverse sign at a certain point, so the magnetic gain is gradually neutralized by the charge. The repetitive magnetic Penrose process is therefore forced to terminate and eventually falls back to the mechanical Penrose process. The energy extraction efficiency $>100\%$ predicted by the single magnetic Penrose process will therefore be prevented.