A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration

TL;DR

This paper introduces a kinematic framework for gravitational lensing using new formulas for refractive index and acceleration derived from the Schwarzschild metric, enabling accurate predictions of light deflection and time delay.

Contribution

It presents novel formulas for refractive index and acceleration in gravitational fields, integrating them into a kinematic approach for lensing analysis.

Findings

Accurate calculation of light deflection and time delay.

Reproduction of caustic patterns in strong and weak lensing.

Validation against standard approximations.

Abstract

This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays, in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray-shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer-plane caustic patterns for multiple masses.