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My Prof told me today there is a 1-1 correspondence between particles in a curved space time, and optics problems in various indices of refraction, extending even as far as black holes. Does anyone have more information on this?

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Your prof seems to be right. The general idea stems from an analogy between refractive index gradients and spacetime curvature. To construct the correspondence it's necessary to postulate constitutive relations for the vacuum that are anisotropic and thus represented by tensors, and that are nonlinear. Of course it becomes more complicated when both electrodynamics and gravity are taken into consideration, but the analogy can be built.

Here are some good resources:

General relativity in electrical engineering

General Relativity without Curved Space-Time

An equivalence principle for electromagnetics through Clifford’s geometric algebras

Effective metrics and a fully covariant description of constitutive tensors in electrodynamics

Matter Waves in a Static Gravitational Field

Matter waves in a gravitational field: An index of refraction for massive particles in general relativity

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  • $\begingroup$ This could use some additional commentary, as per the usual policy. $\endgroup$ – Emilio Pisanty May 28 at 3:46
  • $\begingroup$ Thanks, I've added commentary. $\endgroup$ – S. McGrew May 28 at 4:03
  • $\begingroup$ Perfect thanks so much $\endgroup$ – Craig May 28 at 16:51

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