Ghosts in Massive Gravity

TL;DR

This paper shows that Lorentz-invariant massive gravity around heavy sources inevitably develops ghost instabilities in the Goldstone sector, appearing at distances well beyond the Vainshtein radius and persisting despite nonlinear FP tunings. Using the Stückelberg formalism, unitary gauge, and ADM analysis, the authors demonstrate that higher-derivative kinetic terms generate a sixth, ghostly degree of freedom that cannot be consistently removed by any non-linear extension. The ghost mass is background-dependent and drops near the Vainshtein scale, rendering the theory unreliable inside that region and preventing GR from being recovered in a controlled way. The results suggest fundamental inconsistencies in this class of theories and indicate the need for alternative (e.g., Lorentz-violating) constructions or UV completions to achieve a healthy modification of gravity.

Abstract

In the context of Lorentz-invariant massive gravity we show that classical solutions around heavy sources are plagued by ghost instabilities. The ghost shows up in the effective field theory at huge distances from the source, much bigger than the Vainshtein radius. Its presence is independent of the choice of the non-linear terms added to the Fierz-Pauli Lagrangian. At the Vainshtein radius the mass of the ghost is of order of the inverse radius, so that the theory cannot be trusted inside this region, not even at the classical level.