A note on Harmonic Gauge(s) in Massive Gravity

TL;DR

This paper explores the harmonic gauge in linearized massive gravity, showing that a specific gauge choice yields a consistent five-degree-of-freedom theory without the vDVZ discontinuity, offering new insights into gauge conditions in massive gravity.

Contribution

It demonstrates that the harmonic gauge condition in massive gravity can be physically motivated and leads to a consistent theory with the correct degrees of freedom, avoiding the vDVZ discontinuity.

Findings

A particular harmonic gauge choice yields five degrees of freedom in massive gravity.

The theory avoids the vDVZ discontinuity unlike standard Fierz-Pauli theory.

Harmonic gauge conditions form a class, not a single fixed gauge.

Abstract

We consider the harmonic gauge condition in linearized gravity, seen as a gauge theory for a symmetric tensor field. Once the harmonic gauge condition is implemented, as customary, according to the Faddeev-Popov procedure, the gauge fixed action still depends on one gauge parameter. Consequently, the harmonic gauge appears to be a class of conditions, rather than a particular one. This allows to give a physical motivation for the covariant harmonic gauge(s), which emerges when the gravitational perturbation is given a mass term. In fact, for a particular choice of harmonic gauge, we find a theory of linearized massive gravity displaying five degrees of freedom, as it should, and which is not affected by the vDVZ discontinuity, differently from what happens in the standard Fierz-Pauli theory.