Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-06-20
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, Eq. (1.2) is corrected. arXiv admin note: substantial text overlap with arXiv:0911.0614
Scientific paper
We consider variation of energy of the light-like particle 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. This method is shown to not lead to violation of conformity of varied curve to the null path in contradistinction of the interval variation. Though found equations are differ from standard form of geodesics equations, for the Schwarzschild space-time their solutions coincide with each other to within parameter of differentiation.
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