Is there a trade-off relation between efficiency and power in a collisional Penrose process in an extreme Reissner-Nordstr\"{o}m spacetime?

Abstract

We investigate the power of a collisional Penrose process with an unbound energy extraction from an extreme Reissner-Nordstr\"{o}m black hole. This process takes infinite time in a time coordinate at a constant radial coordinate outside of the black hole. For black holes as a power plant, the power of the process for an observer far away from the black hole can be useful. We define the power as energy gain from the extreme Reissner-Nordstr\"{o}m black hole divided by the time interval of the process in a coordinate time; we estimate the upper bound of the power in a near-horizon limit, while the efficiency of the process can be arbitrary large in that limit. Thus, we conclude that there is no trade-off relation between the efficiency and power in the collisional Penrose process in extreme Reissner-Nordstr\"{o}m spacetime.