Well-posedness of minimal dRGT massive gravity

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.