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Gravitational light deflection in flat spacetime using effective refractive indexes: a derivation in full agreement with Einstein’s prediction

Author:

Roux, Jean-Claude

Category:

Research Papers

Sub-Category:

Relativity Theory

Language:

English

Date Published:

May 18, 2025

File:

/Research Papers-Relativity Theory/Download/10160

Downloads:

472

Keywords:

General relativity; geometric optics; refractive index; light beam; Schwarzschild radius; flat space-time; Newtonian gravity; weak gravitational field; angular light deviation

Abstract:

This paper introduces a new approach to modelling gravitational light deflection using a gravitational refractive index. In the first section, light deflection is derived using Newtonian mechanics, leading to the well-known result of gravitational lensing. The second section extends this approach to geometric optics by introducing a gravitational refractive index, previously used for modelling Shapiro’s time delay, and shows how the combination of both contributions results in the Einstein’s prediction for light deflection. The third section derives a key relationship from the Lagrangian formulation. In the fourth section, the trajectory equation is solved and the light deflection angle is confirmed. Finally, in the fifth section, the correct adaptive choice of the refractive index is justified for both the Shapiro’s time delay (temporal component) and gravitational lensing (temporal and radial components), ultimately leading to the Einstein’s result for gravitational light deflection in a weak gravitational field.

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