Charged particle trajectories in a toroidal magnetic and rotation-induced electric field around a black hole

Abstract

Trajectories of charged particles in a combined poloidal, toroidal magnetic field and a rotation-induced unipolar electric field superposed on a Schwarzschild background geometry have been investigated extensively in the context of accreting black holes. The main purpose of this paper is to obtain a reasonably good insight on the effect of spacetime curvature on the electromagnetic field surrounding black holes. The coupled equations of motion have been solved numerically and the results have been compared with that for flat spacetime. It is found that the toroidal magnetic field dominates the induced electric field in determining the motion of charged particles in curved spacetime. The combined electromagnetic field repels a charged particle from the vicinity of a compact massive object and deconfines the particle from its orbit. In the absence of a toroidal magnetic field the particle is trapped in a closed orbit. The major role of gravitation is to reduce the radius of gyration significantly while the electric field provides an additional force perpendicular to the circular orbit. Although the effect of inertial frame dragging and the effect of magnetospheric plasma have been neglected, the results provide a reasonably good qualitative picture of the important role played by gravitation in modifying the electromagnetic field near accreting black holes and hence the results have potentially important implications on the dynamics of the fluid and the radiation spectrum associated with accreting black holes.