Localized gravitational energy in a Schwarzschild field

TL;DR

This paper proposes a localized scalar function for gravitational energy in general relativity, linking mass increase to gravitational potential and explaining energy transfer in dynamic fields, independent of coordinate choices.

Contribution

It introduces a new interpretation of gravitational energy as a localized scalar function, providing a physical basis for energy transfer in dynamic gravitational fields.

Findings

Bodies falling in Schwarzschild field follow relativistic mass-energy relations.

Time-varying fields induce net energy transfer between bodies.

Energy localization is independent of coordinate system choices.

Abstract

An interpretation of general relativity is developed in which the energy used to lift a body in a static gravitational field increases its rest mass. Observers at different gravitational potentials would experience different mass reference frames. It is shown that bodies falling in a Schwarzschild field exhibit the relativistic mass/energy relationship from special relativity. This new result is independent of the choice of coordinates. The proposed approach provides a physical explanation for gravitational energy, which is localized as a scalar function intrinsic to general relativity. Applying this model to the Robertson-Walker metric demonstrates that time-varying fields induce a net energy transfer between bodies that is not exhibited in static fields.