Well-posedness of minimal dRGT massive gravity

TL;DR

This paper develops a new harmonic and first-order formulation of minimal dRGT massive gravity, demonstrating strong hyperbolicity near Minkowski space, which suggests well-posedness of the Cauchy problem for this theory.

Contribution

It introduces a strongly hyperbolic formulation of minimal dRGT massive gravity, supporting its classical well-posedness near Minkowski backgrounds.

Findings

The theory admits a strongly hyperbolic formulation around Minkowski space.

Characteristics of the graviton mode are governed by the inverse metric.

Conjecture that Cauchy evolution remains well-posed near Minkowski background.

Abstract

Ghost-free dRGT massive gravity is a subtle theory, even at the classical level. Its viability depends on Vainshtein screening, which is an intrinsically non-linear phenomenon, and thus understanding the full non-linear dynamics of the theory is crucial. The theory was not expected to have a well-posed hyperbolic formulation as it is usually interpreted as a low energy EFT, and hence its short distance physics would be modified by higher derivative operators. Here we study a new dynamical formulation of the theory for the case of the minimal mass term. This firstly involves using a harmonic formulation of the theory, and then writing it as a first order system. We are able to cast it in a form that is strongly hyperbolic about the Minkowski background. We discuss strong hyperbolicity for backgrounds close to the Minkowski solution, conjecturing that Cauchy evolution remains well-posed. Interestingly, as part of the analysis, we find that the characteristics of the spin two graviton mode are simply governed by the inverse metric on a general background.