Fokker's type action at a distance theory of gravitation

Physics

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Fokker-Planck Equation, Gravitation Theory, Gravitational Waves, Particle Interactions, Particle Motion, Einstein Equations, Electrodynamics, Equations Of Motion, Many Body Problem, Riemann Manifold, Space-Time Functions

Scientific paper

An attempt is made to develop a theory of direct gravitational interaction of an arbitrary order, i.e., a many-particle interaction. The situation considered is that of a moving particle in a fixed Riemannian space-time which interacts with a system characterized by a definite energy momentum tensor. A linear formulation of the Fokker type action is used to define particle equations of motion in a geodesic form in a metric of arbitrary order. A proof is developed to show that the resulting metric satisfies the Einstein equations and is commensurate with the Lorentz gauge in Wheeler-Feynman electrodynamics. When applied to many-particle interactions, the absorber theory of gravitational radiation that has been defined is effective only for a linear approximation solution to the Einstein equation, and will require further work to serve as a general absorber theory.

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