Abstract
We investigate the gravitational and electromagnetic fields on the generalized Lagrange space endowed with the metricg ij(x, y) = γij(x) + {1 + 1/n 2 (x, y)}y iyj. The generalized Lagrange spacesM m do not reduce to Lagrange spaces. Consequently, they cannot be studied by methods of symplectic geometry. The restriction of the spacesM m to a sectionS ν(M) leads to the Maxwell equations and Einstein equations for the electromagnetic and gravitational fields in dispersive media with the refractive indexn(x, V) endowed with the Synge metric. Whenn(x, V) = 1 we have the classical Einstein equations. If 1/n 2=1−1/c 2 (c being the light velocity), we get results given previously by the authors. The present paper is a detailed version of a work in preparation.
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Miron, R., Kawaguchi, T. Relativistic geometrical optics. Int J Theor Phys 30, 1521–1543 (1991). https://doi.org/10.1007/BF00675616
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DOI: https://doi.org/10.1007/BF00675616