Gravity with more or less gauging

TL;DR

This paper explores various formulations of General Relativity with different gauge invariances, highlighting their local equivalence and differences in global properties through the concepts of inessential gauge invariance and symmetry trading.

Contribution

It introduces the idea of inessential gauge invariance and demonstrates how different formulations of gravity are linked through symmetry trading and linking theories.

Findings

Different formulations are locally equivalent but may differ globally.

Examples include the dilaton and unimodular formulations of GR.

The paper discusses these concepts in both Lagrangian and Hamiltonian formalisms.

Abstract

General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation where it is only invariant under the smaller group of special diffeomorphisms. Other formulations with the same number of gauge generators, but a different gauge algebra, also exist. These different formulations provide examples of what we call 'inessential gauge invariance', 'symmetry trading' and 'linking theories'; they are locally equivalent, but may differ when global properties of the solutions are considered. We discuss these notions in the Lagrangian and Hamiltonian formalism.