Abstract

The strong similarities between gravitational lensing and conventional optical lensing are considered, and a graded vacuum refractive index description of the propagation of light in a gravitational field is proposed. By comparing the Fermat principle in conventional optics and the Schwarzschild metric in general relativity, we obtained the exact exterior and interior solutions of this refractive index for a static spherically symmetric gravitational field. In the weak field case, the two solutions approach a simple unified exponential function of the gravitational potential. The result is used to analyse gravitational lensing in a conventional optical way.

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