Second-order time delay by a radially moving Kerr-Newman black hole

TL;DR

This paper derives an analytical expression for the second-order time delay of light near a moving Kerr-Newman black hole, accounting for velocity effects, and discusses potential observational detection of these corrections.

Contribution

It provides the first derivation of second-order time delay for light near a moving Kerr-Newman black hole, including velocity effects, extending previous first-order results.

Findings

Derived compact second-order time delay formula

Confirmed agreement with previous first-order formulations

Analyzed the magnitude and detectability of velocity-induced corrections

Abstract

We derive the analytical time delay of light propagating in the equatorial plane and parallel to the velocity of a moving Kerr-Newman black hole up to the second post-Minkowskian order via integrating the null geodesic equations. The velocity effects are expressed by a very compact form. We then concentrate on analyzing the magnitudes of the correctional effects on the second-order contributions to the delay and discuss their possible detection. Our result in the first post-Minkowskian approximation is in agreement with Kopeikin and Sch\"{a}fer's formulation which is based on the retarded Li\'{e}nard-Wiechert potential.