Second order Kerr-Newman time delay

The explicit form for the post-Newtonian gravitational time delay of light signals propagating on the equatorial plane of a Kerr-Newman black hole is derived. Based on the null geodesic in Kerr-Newman spacetime, we adopt the iterative method to calculate the time delay. Our result reduces to the previous formulation for the Kerr black hole if we drop the contribution from the electrical charge. Our time-delay formula for the Reissner-Nordstrom geometry is different from the previous publication [Phys. Rev. D 69, 023002 (2004)], in which the largest second order contribution to the time delay is missing.