Isofrequency pairing of circular orbits in Schwarzschild spacetime in the presence of magnetic field

Abstract

We study isofrequency pairing of the circular non-geodesic orbits in the vicinity of the Schwarzschild black hole immersed in external asymptotically uniform magnetic field. The dependence of the isofrequency pairing of non-geodesic orbits from the special quantities, such as radius of the innermost stable circular orbits (ISCO), radius of the circular orbits (r b ) at the limit e(eccentricity)→0, and from the value of the small quantity ξ=(r b −r ISCO) of the particles moving around the Schwarzschild black hole in the presence of the magnetic field has been found. It is shown that presence of the magnetic field gives rise to the r ISCO and r b of the particles to be slightly shifted from black hole and the contribution of the quantity ξ decreases the amount of isofrequency pairing of non-geodesic orbits due to the reduction of the surface of the region between the separatrix and circular-orbit duals (COD). We study the dependence of surface of region where particles can move and isofrequency pairing of non-geodesic orbits occur around the Schwarzschild black hole from the magnetic field. We find a decrease of nearly (7–10) % for the maximal values of the magnetic field B∼106–107 Gauss in the surface of region where isofrequency pairing occurs around central object with compare to the one around Schwarzschild black hole without magnetic field. This result implies that it makes easier to identify signals through the astrophysical observations of compact objects in the presence of magnetic field.