General properties of the electric Penrose process

We consider the Penrose process with the charged particles in the Reissner-Nordstr\"{o}m background. Let parent particle 0 decay to particles 1 and 2. With the assumption that all three particles move in the same 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 E₁ or E₂ of daughter particles with respect to the angular momentum L₁ or L₂ of one of them. We derive bounds on the values of angular momenta L₁ and L₂. We give classification of these scenarios and discuss their properties including decay in the near-horizon region. 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 m₀→ ∞, 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.