The Problem of Particle Motion in the Schwarzschild Field: Critical Methodological Analysis, Exact Numerical Solution, and Links to Physics Frontiers
Résumé
The problem of Schwarzschild dynamics is of fundamental importance in Modern Physics since the Schwarzschild solution is considered the exact one to the Einstein field equation and it is directly testable, in theory. It is widely believed that the solution (a planetary perihelion advance prediction) is flawless and successfully passed the observational test what eventually put General Relativity to the rank of the only true relativistic theory of gravitational field. In this work, we critically analyze the GR prediction methodology and investigate physical meaningfulness of the solution, particularly, in view of relationship of proper versus coordinate time variables and their connections with a relativistic mass and energy concepts. Our results of exact numerical solution to the problem play an essential role in the methodological analysis and assessments. The overall conclusion is made that the GR dynamic equation for point particle motion from Schwarzschild metric is prone to inner contradictions inherited from the GR Physical Foundations. In particular, its exterior solution admits superluminal motion. Strictly speaking, it cannot be used for a treatment of observational data. The work consists of two parts: the first one is devoted to the critical analysis of the Schwarzschild dynamics methodology and the numerical results, the second one to the relevant links with Physics Frontiers. Alternative approach based on a field-dependent proper mass concept is discussed.
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