Application of Lagrange mechanics for analysis of the light-like particle motion in pseudo-Riemann space

Details Application of Lagrange mechanics for analysis of the light-like particle motion in pseudo-Riemann space Application of Lagrange mechanics for analysis of the light-like particle motion in pseudo-Riemann space

2009-11-03

arxiv.org/abs/0911.0614v13

Int. J. Th. Math. Phys. N2, V2 (2012), 10-15

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, Corrected typos

Scientific paper

10.5923/j.ijtmp.20120202.03

We consider variation of energy of the light-like particle in non-covariant form in Riemann space-time, find lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance with principles of the calculus of variations in mechanics. Their solutions are found for metrics of Schwarzschild, FLRW model for the flat space and Goedel. For these spaces effective mass of light-like particle is established. Relativistic analog of inertial mass for photon is determined in central gravity field in empty space.

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