Localized gravitational energy in a Schwarzschild field

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.