Ghosts in Massive Gravity

TL;DR

This paper demonstrates that Lorentz-invariant massive gravity theories exhibit ghost instabilities around heavy sources, which appear at large distances and undermine the theory's classical consistency.

Contribution

It reveals the universal presence of ghost instabilities in classical solutions of Lorentz-invariant massive gravity, regardless of non-linear term choices.

Findings

Ghosts appear at large distances from sources, beyond the Vainshtein radius.

Ghost mass is inversely proportional to the radius at the Vainshtein scale.

The instability persists regardless of non-linear modifications to the theory.

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.