Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-08-02
Annalen Phys.15:877-893,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Accepted in Annalen der Physik
Scientific paper
10.1002/andp.200610218
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for thederivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a nonlinear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the $N$-body problem of the Lorentz invariant field equations.
Itin Yakov
Kaniel Shmuel
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