Bound chaotic photon orbits in a magnetized Kerr–Newman spacetime

Abstract

Unlike those in the nonmagnetized counterpart, equatorial photon effective potentials outside the horizons allow for the existence of closed pockets or potential wells corresponding to local minimum values in a magnetized Kerr–Newman spacetime of Gibbons et al. There are three bound photon orbits, which neither fall into the black hole nor escape to infinity. They are stable circular orbits, bound quasiperiodic orbits and bound chaotic orbits. The stable circular photon orbits and bound quasiperiodic photon orbits are allowed on and outside the equatorial plane, but the bound chaotic photon orbits are only allowed outside the equatorial plane. On the other hand, the photon effective potentials have potential barriers with local maximum values in the magnetized case, similar to those in the nonmagnetized case. This fact means the existence of three other photon orbits, which include the photons falling to the center, scattering to infinity and unstably circling in the center. They are not necessarily restricted to the equatorial plane, either. The six types of photon orbits are confirmed numerically via an explicit symplectic integrator and the techniques of fast Lyapunov indicators and 0–1 test correlation method. In particular, a number of bound quasiperiodic photon orbits and bound chaotic photon orbits are found. The method for finding these six types of photon orbits in the phase space will also be used as a new ray-tracing method to find the corresponding six regions on the observer’s plane and to obtain black hole shadows.