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 theϑ-equation does not yield the first integral forϑ ≠π/2. We have however considered circular orbits about the axis forϑ=constant ≠π/2 by requiring bothϑ andr to remain fixed all through the motion. Forϑ ≠π/2 orbits, in contrast to the similar classical situation, there occur forbiddenϑ-ranges. This seems to be a relativistic effect.
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Chellathurai, V., Dhurandhar, S.V. & Dadhich, N. Charged particle orbits in the field of two charges placed symmetrically near a schwarzschild black hole. Pramana - J Phys 27, 485–495 (1986). https://doi.org/10.1007/BF02846876
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DOI: https://doi.org/10.1007/BF02846876