Gravitational time delay effects by Kerr and Kerr-Newman black holes in strong field limits

TL;DR

This paper analytically investigates the gravitational time delay caused by Kerr and Kerr-Newman black holes in strong field limits, revealing how mass, spin, and charge influence the delay between relativistic images.

Contribution

It develops an analytical formalism for calculating light travel time delays in strong gravitational lensing by Kerr and Kerr-Newman black holes, including effects of charge and spin.

Findings

Higher black hole mass or extreme spin increases time delay.

Black hole charge enhances delay for opposite-side images with mixed orbits.

Charge reduces delay for same-side images with uniform orbits.

Abstract

We study the time delay between two relativistic images due to strong gravitational lensing of the light rays caused by the Kerr and Kerr-Newman black holes. The trajectories of the light rays are restricted on the equatorial plane. Using the known form of the deflection angle in the strong deflection limit (SDL) allows us to analytically develop the formalism for the travel time of the light from the distant source winding around the black hole several times and reaching the observer. We find that the black hole with higher mass or with spin of the extreme black hole potentially have higher time delay. The effect of the charge of the black hole enhances the time delay between the images lying on the opposite side of the optical axis resulting from the light rays when one light ray is in the direct orbit and the other is in the retrograde orbit. In contrary, when both light rays travel along either direct or retrograde orbits giving the images on the same side of the optical axis, the charge effect reduces the time delay between them. We then examine the time delay observations due to the galactic and supermassive black holes respectively