Charged particle orbits in the field of two charges placed symmetrically near a schwarzschild black hole

Abstract

From the Copson and Linet solution for the electrostatic field due to a point charge near a Schwarzschild black hole, we have deduced the field due to two equal charges placed symmetrically (diametrically opposite) about the hole. It turns out that the motion of a test-charged particle is completely solvable only in the equatorial plane, because the θ -equation does not yield the first integral for θ ≠ π /2. We have however considered circular orbits about the axis for θ=constant ≠ π /2 by requiring both θ and r to remain fixed all through the motion. For θ ≠ π /2 orbits, in contrast to the similar classical situation, there occur forbidden θ-ranges. This seems to be a relativistic effect.