Second Order Kerr-Newman Time Delay

TL;DR

This paper derives an explicit post-Newtonian gravitational time delay formula for light signals near Kerr-Newman black holes, including charge effects, improving previous models by accounting for second-order contributions.

Contribution

It provides a new, more complete second-order time delay formula for Kerr-Newman black holes, extending previous Kerr and Reissner-Nordström models.

Findings

Derived explicit second-order time delay formula for Kerr-Newman spacetime.

Reduced to Kerr black hole case when charge is zero.

Identified missing second-order term in previous Reissner-Nordström studies.

Abstract

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 Kerr black hole if we drop off the contribution from the electrical charge. Our time-delay formula for the Reissner-Nordstr\"{o}m 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.