Trajectory of a light ray in Kerr field: A material medium approach

TL;DR

This paper investigates the deflection of light in Kerr gravitational fields using a material medium approach, focusing on refractive index calculations that incorporate frame dragging effects, and compares results with traditional null geodesic methods.

Contribution

It extends the material medium approach to Kerr fields, including frame dragging, providing an alternative method for calculating light deflection in rotating black hole spacetimes.

Findings

Refractive index in Kerr field was derived considering frame dragging.

Light deflection in Kerr field was calculated and compared with null geodesic results.

The approach offers an alternative perspective on gravitational lensing in rotating spacetimes.

Abstract

The deflection of light ray as it passes around a gravitational mass can be calculated by different methods. Such calculations are generally done by using the null geodesics under both strong field and weak field approximation. However, several authors have studied the gravitational deflection of light ray using material medium approach. For a static, non-rotating spherical mass, one can determine the deflection in Schwarzschild field, by expressing the line element in an isotropic form and calculating the refractive index to determine the trajectory of the light ray. In this paper, we draw our attention to the refractive index of light ray in Kerr field using the material medium approach. The frame dragging effects in Kerr field was considered to calculate the velocity of light ray and finally the refractive index in Kerr field geometry was determined. Hence the deflection of light ray in Kerr field was calculated, assuming far field approximation and compared the results with those calculations done earlier using Null geodesics.