Matter waves in a gravitational field: An index of refraction for massive particles in general relativity
Abstract
We consider the propagation of massive-particle de Broglie waves in a static, isotropic metric in general relativity. We demonstrate the existence of an index of refraction that governs the waves and that has all the properties of a classical index of refraction. We confirm our interpretation with a WKB solution of the general-relativistic Klein-Gordon equation. Finally, we make some observations on the significance of the optical action.
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