Nature of the Gravitational Field and its Legitimate Energy-Momentum Tensor

TL;DR

This paper explores various geometric representations of the gravitational field, introduces a field-based approach in Minkowski spacetime, and derives a legitimate energy-momentum tensor consistent with Einstein's equations and energy concepts.

Contribution

It presents a novel formulation of gravity as a field in Minkowski spacetime with explicit Lagrangian and Maxwell-like equations, and identifies a valid energy-momentum tensor for the gravitational field.

Findings

Equivalent Maxwell-like field equations to Einstein's equations

A new legitimate energy-momentum tensor for gravity

Geometric and field-based representations of gravitational fields

Abstract

In this paper we show how a gravitational field generated by a given energy-momentum distribution (for all realistic cases) can be represented by distinct geometrical structures (Lorentzian, teleparallel and non null nonmetricity spacetimes) or that we even can dispense all those geometrical structures and simply represent the gravitational field as a field, in the Faraday's sense, living in Minkowski spacetime. The explicit Lagrangian density for this theory is given and the field equations (which are a set of four Maxwell's like equations) are shown to be equivalent to Einstein's equations. We also analyze if the teleparallel formulation can give a mathematical meaning to "Einstein's most happy thought", i.e. the equivalence principle. Moreover we discuss the Hamiltonian formalism for for our theory and its relation to one of the possibles concepts for energy of the gravitational field which emerges from it and the concept of ADM energy. One of the main results of the paper is the identification in our theory of a legitimate energy-mometum tensor for the gravitational field expressible through a really nice formula.