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Snell's Law and Superposition of charge

There exists an isomorphism (one-to -one mapping) between Snell's Law of refractive index of material (angle of refraction is a function of the incidence angle) and the use of a curved (rather than flat) metric to capture the bending of light. That the isomorphism exists is because of the general co variance of Maxwell's Equations.

A few thoughts in increasing tentativeness:

1Does this isomorphism require also the linearity (superposition of charges) of the electromagnetic waves or can we also infer that we could similarly cloak non linear gravitational waves by an appropriate mass distribution given the natural covariance of einstein's field equations?

2 Do we need such additional inertial (gravitational) mass cloaking if there were to be some (albeit) contrived ( annulus type but need not be charged) mass distribution out in the cosmos to account for some missing (dark) matter?

3 and on the annulus mass formation alluded to in talk is it not the case that the inertial mass according to Mach and Brans-dicke and the likes should be determined from the annulus of all the (receding) stars in the universe. Just a thought is there no such Machian equivalent principle for magnetic ( if not electric) charge where overall neutrality need not be the case in bulk matter distributions?


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