A paper appeared in Classical and Quantum Gravity.
Co-author, Associate Professor of the Department of Relativity Theory and Gravity of KFU Alexei Zayats explains, “Light is distributed linearly in flat space-time. In space-time curvature, according to general relativity, light must be distributed along isotropic geodesic lines.
“In our publication, we studied distribution of light within the non-minimal Einstein-Maxwell theory. From a geometric optics standpoint, in this model, which takes account of the interaction between the electromagnetic field and space-time curvature, light is distributed as if it passes through an anisotropic quasi-medium. As a result, the situation becomes more complex, and different optical effects may arise, such as double refraction.”
In the paper, Dr. Zayats and Professor Alexander Balakin show that with certain limitation on the space-time metric, a full classification of possible dispersion relations and surfaces can be constructed. As the researchers state, there are only seven such types, including the trivial case of light being distributed exactly as in vacuum.
“Among non-trivial types, two can be singled out: the first is where the quasi-medium generated by an interaction with the curvature has the same properties as a uniaxial crystal; the second one is where the quasi-medium looks like a biaxial crystal. In all other cases, the dispersion relations do not have analogues in crystal optics.”