Proper Mass Variation under Gravitational and Coulomb Force Action in Relativistic Mechanics of Point Particle

The problem studied is formulated in the title: proper mass variation under gravitational and Coulomb force action in Relativistic Mechanics of point particle. The novelty is that equations of motion are obtained in the relativistic Lagrangean framework for conservative force fields under assumption of field dependent proper mass. The dependence of proper mass on field strength is derived from the equations of particle motion. The result is the elimination of a classical 1/r divergence. It is shown that a photon in a gravitational field may be described in terms of a refracting massless medium. This makes the gravity phenomenon compatible with SR Dynamic framework. New results concerning gravitational properties of particle and photon, as well as an experimental test of predicted deviation from 1/r^2 classical Coulomb force law are discussed. The conclusion is made that the approach of field-dependent proper mass is perspective for better understanding GR problems and further studies on divergence-free field theory development. Key words: Relativity; gravity; Coulomb; particle; photon; speed of light; proper mass variation. PACS: 03.30.+p, 04.20.-g