American Journal Of Physics
Science, Technology and Society
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 Wentzel-Kramers-Brillouin solution of the general-relativistic Klein-Gordon equation. Finally, we make some observations on the significance of the optical action.
Evans, James C., Pm Alsing, S. Giorgetti, and K. K. Nandi. 2001. "Matter waves in a gravitational field: An index of refraction for massive particles in general relativity." American Journal Of Physics 69(10): 1103-1110.