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
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$\begingroup$ This could use some additional commentary, as per the usual policy. $\endgroup$ Commented May 28, 2019 at 3:46
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