General properties of the electric Penrose process

We consider the Penrose process with the charged particles in the Reissner-Nordstr\"{o}m (RN) background. Let parent particle 0 decay to particles 1 and 2. With the assumption that all three particles move in the equatorial plane, the exact formulas for characteristics of particles 1 and 2 in terms of those of particle 0 are derived. We concentrate on scenarios in which particle 1 and 2 are ejected along the trajectory of particle 0. It is shown that such scenarios correspond to the extrema of energies $E_{1}$ or $E_{2}$ of daughter particles with respect to the angular momentum $L_{1}$ or $L_{2}$. We derive bounds on the values of angular momenta $L_{1}$ and $% L_{2}$. We give classification of these scenarios and discuss their properties including decay in the near-horizon region. We find that the maximum of efficiency is achieved on the horizon for some of these scenarios but not for all of them and with additional constraints on particle parameters. The results are reformulated in terms of velocities of daughter particles in the center of mass frame. The approach is applicable also to collisional Penrose process, in which a combination of particles 1 and 2 is considered as one effective particle. If the mass of particle 0 $% m_{0}\rightarrow \infty $, the situation corresponds to the Ba\~{n}% ados-Silk-West effect, the results agree with the ones known in literature before. In addition, we consider special cases when decay occurs in the turning point for one or all three particles. The formalism developed in this work has a model-independent character and applies not only to the RN metric.