Dynamics of an electric current-carrying string loop near a Schwarzschild black hole embedded in an external magnetic field

Abstract

We study motion of an electric current-carrying string loop oscillating in the vicinity of the Schwarzschild black hole immersed in an external uniform magnetic field. The dependence of boundaries and different types of motion of the string loop on magnetic field strength is found. The dynamics of the string loop in the Cartesian xy plane depends both on value and direction of the magnetic field and current. It is shown that the magnetic field influence on the behavior of the string loop is quite significant even for weak magnetic field strength. The oscillation of the string loop becomes stronger or weaker in dependence on the direction of the Lorenz force. We illustrate the various regimes of the trajectories of the string loop that can fall down into the black hole, escape to infinity, or be trapped in the finite region near the horizon for the different representative values of the magnetic field. We have also considered the flat spacetime limit as the condition of the escape of the string loop from the neighborhood of the black hole to infinity. We found the expression for the magnetic field strength for which the oscillatory motion of the string loop totally vanishes and the string loop can have maximal acceleration in the perpendicular direction to the plane of the loop.