An axiomatic purification of gravity

TL;DR

This paper develops a new axiomatic framework for gravity called purified gravity, deriving it from conservation laws and equivalence principles, and links it to massive electromagnetism with a unique action principle.

Contribution

It introduces a premetric axiomatic approach to gravity, leading to a unique theory of Coincident General Relativity with novel insights into the metric and graviton.

Findings

The theory is uniquely fixed by an action principle.

The formalism draws an analogy with massive electromagnetism.

The metric and graviton are interpreted as a Stueckelberg field and Goldstone boson.

Abstract

A theory of gravity is deduced from the axioms of the premetric program. The starting point is the conservation of energy and momenta, and the equivalence of gravitation and inertia. The latter is what leads to the framework of the so called purified gravity. The local and linear constitutive relation has 14 components when it is assumed to be metrical, but the compatibility of the constitutive relation with an action principle fixes uniquely the theory of Coincident General Relativity. The premetric formalism of purified gravity has a direct analogy with massive electromagnetism, the Planck mass corresponding to the Proca mass of the gauge boson. The metric emerges as a Stueckelberg field, and the graviton as a Goldstone boson of the broken symmetry.