Axiomatic derivation of coincident general relativity and its premetric extension

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.