Charged-particle motion around a rotating non-Kerr black hole immersed in a uniform magnetic field

Abstract

We present analytical solutions of Maxwell's equations around a rotating non-Kerr black hole immersed in an external uniform magnetic field. The influence of a magnetic field on the effective potential of the radial motion of a charged test particle around a rotating non-Kerr black hole immersed in an external magnetic field are investigated by using the Hamilton-Jacobi equation of motion. The dependence of the minimal radius of the circular orbits ${r}_{\mathrm{mc}}$ and the radius of the innermost stable circular orbits (ISCOs) from the deformation and the magnetic parameters for the motion of charged particles around a rotating non-Kerr black hole are also presented. An increase of the magnetic field decreases the ISCO radius, while the negative deformation parameter may lead to a larger ISCO radius. A comparison of the numerical results of ISCOs around a non-Kerr black hole with the observational data for the ISCO radius of rapidly rotating black holes [R. Shafee et al., Astrophys. J. 636, L113 (2006)] provides the upper limit for the deformation parameter as $ϵ\ensuremath{\le}22$.