On an Alternative Approach to Gravitation

TL;DR

This paper explores alternative energy-momentum tensors for gravity, compares their properties in the Newtonian limit, and constructs Lagrangians for a spin-2 field, proposing a tensor suitable for explaining perihelion shift and discussing implications for strong-field modifications.

Contribution

It introduces a new energy-momentum tensor for gravity that aligns with perihelion shift observations and develops Lagrangians for spin-2 fields differing by divergences, offering a novel approach to gravitational energy-momentum.

Findings

Different energy-momentum tensors distribute gravitational energy differently.

Only one tensor explains the perihelion shift effectively.

Phenomenological approach may modify gravity in strong fields.

Abstract

Several energy-momentum "tensors" of gravitational field are considered and compared in the lowest approximation. Each of them together with energy-momentum tensor of point-like particles satisfies the conservation laws when equation of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from the other in the way their energy density is distributed between energy density of interection (nonzero only at locations of particles) and energy density of gravitational field. Starting from Lorentz invariance the Lagrangians for spin-2, mass-0 field are constracted. They differ only by divergences. From these Lagrangians by Belinfante-Rosenfeld procedure the energy-momentum tensors are build. Only one of them is suitable for explaining the perihelion shift. This tensor does not coincide with Weinberg`s one (directly obtainable from Einstein equation). It is noted that phenomenological field-theoretical approach (utilizing only vertices and propagators) can lead to modification of theory in the region of strong field, where till now no observational data are available.