Gravitational Lensing Analyzed by Graded Refractive Index of Vacuum

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.

Added an appendix for deriving Eqs. (11) and (12) in detail

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• On geodesics of gradient-index optical metrics and the optical-mechanical analogy
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• Two-dimensional Dirac matter in the semiclassical regime
• Optical analogues to the Kerr-Newman black hole