Nonlinear Newtonian theory and the effect of time dilatation

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Gravitation Theory, Newton Theory, Time, Differential Equations, Gravitational Fields, Nonlinear Equations, Spheres, Stretching

Scientific paper

The fact that energy density ρg of a static spherically symmetric gravitational field acts as a source of gravity, gives a harmonic function f(φ) = exp(φ/c2), which is determined by a nonlinear differential equation presented in the paper. Furthermore, the author formulates the infinitesimal time-interval between a couple of events measured by two different inertial observers, one in a position with potential φ - i.e., dtφ and the other in a position with potential φ = 0 - i.e., dt0, as dtφ = fdt0. When the principle of equivalence is satisfied, the well-known effect of time dilatation is obtained.

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