Analytical derivation of second-order deflection in the equatorial plane of a radially moving Kerr-Newman black hole

In this work, we base ourselves on the second-order post-Minkowskian equations of motion, and apply an iterative technique to analytically derive the gravitational deflection of the relativistic particles in the equatorial plane of a Kerr-Newman black hole with a radial (or longitudinal) and constant velocity. We find that the kinematically correctional effects on the second-order contributions to the deflection can be expressed in a very compact form, which are valid for both the massive particle and photon. Our result reduces to the previous formulation for the first-order deflection caused by a moving Schwarzschild black hole when the second-order contributions are dropped.