Energy-extraction processes from a Kerr black hole immersed in a magnetic field. II. The formalism

Abstract

This is the second of two papers on energy-extraction processes near a Kerr black hole immersed in a magnetic field. A convenient formalism for discussing energy extraction by the Penrose process is presented. In the formalism a three-dimensional particle space is imagined corresponding to the three particles participating in the process. The energy-extraction process is then described by the dynamics of vectorial quantities pertaining to the parameters of the particles subject to the constraints of momentum and charge conservation. A general scheme is formulated for the matching of the particle parameters at the moment of splitting of the particle. The occurrence of the negative-energy states is investigated with respect to two important parameters, namely, the charge and angular momentum of the particle.