Application of Lagrange Mechanics for Analysis of the Light-Like Particle Motion in Pseudo-Riemann Space

Abstract

Center for Relativity and Astrophysics, 185 Box, 194358, Saint-Petersburg, Russia Abstract We consider variation of energy of the light-like particle in the pseudo-Riemann space-time, find lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in ac- cordance with principles of the calculus of variations in mechanics. This method is compared with the Fermat's principle for the stationary gravity field. The produced equations are solved for the metrics of Schwarzschild, FLRW model for the flat space and Godel. For these spaces effective mass of light-like particle is established. Relativistic analogue of inertial mass for photon is determined in central gravity field in empty space.