Gravitational Lensing Analyzed by Graded Refractive Index of Vacuum

TL;DR

This paper presents a novel optical approach to analyze gravitational lensing by modeling spacetime as a graded refractive index, providing exact solutions and addressing the central image missing problem.

Contribution

It introduces a graded refractive index model for gravitational fields, offering exact solutions and simplifying gravitational lensing analysis compared to traditional methods.

Findings

Derived exact exterior and interior solutions for the refractive index in gravitational fields.

Unified exponential function for weak gravitational fields.

Provided an optical explanation for the missing central image in gravitational lensing.

Abstract

We found strong similarities between the gravitational lensing and the conventional optical lensing. The similarities imply a graded refractive index description of the light deflection in gravitational field. We got a general approach to this refractive index in a static spherically symmetric gravitational field and obtained its exterior and interior solutions exactly through the general relativity. In weak field case, the two solutions come to a simple unified exponential function of the gravitational potential. With these results, the gravitational lensing can be analyzed in a convenient optical way. Especially, the long puzzling problem of the central image missing can be solved easily. We also pointed out that the graded refraction property of the gravitational spacetime is related to the vacuum influenced by the gravitational matter.