Energy Extraction from a Kerr Black Hole via Magnetic Reconnection within the Plunging Region

Magnetic reconnection within a highly magnetized plasma has been seen as a viable mechanism to extract the energy from a rotating black hole, as it can generate negative energy plasmoids in the ergoregion. For a typical accreting black hole, the ergoregion is filled with bulk plasma plunging from the innermost-stable-circular orbit (ISCO). In this study, we present an analytical study of the energy extraction via magnetic reconnection process in the plunging region. In contrast to the toroidal plasma, where the magnetic field cannot be derived from the MHD scheme, the magnetic field in the plunging plasma was determined by the ideal-MHD condition. We derive the global magnetic field structure in a fast reconnection model, and we read the expressions for the energies of plasmoids ejected from the reconnection region, for general stationary and axisymmetric spacetimes. Then, we demonstrate the behaviors of ejected energies varying with the reconnection locations in the Kerr spacetime, and identify the region where a negative-energy plasmoid can be produced. We find that for a certain magnetization there exists a critical value of the black hole spin, beyond which the energy extraction can occur, and the energy extraction is most efficient for the near-extreme black hole. Moreover, we study the conditions necessary for a plasmoid with positive energy to escape to the infinity, a crucial requirement for effective energy extractions. Considering the escaping conditions, we provide the parameter space in the radius-spin plane in which the energy extraction mechanism is effective.