Acausality of Massive Gravity

TL;DR

The work analyzes the causal structure of ghost-free massive gravity in the f-g framework, focusing on the Wess-Zumino five-DoF theory. It applies the method of characteristics to shock-wave discontinuities in the constraints and identifies a contorsion-related term in the scalar constraint as the source of acausality. The main result is that, despite removing the BD ghost, the Wess-Zumino model admits acausal, superluminal characteristics. This suggests a fundamental obstruction to building causal, ghost-free finite-range gravity within this class and informs the viability of related deRham constructions, with cubic-in-f models potentially offering a path forward but remaining unresolved.

Abstract

We show, by analyzing its characteristics, that the ghost-free, 5 degree of freedom, Wess--Zumino massive gravity model admits superluminal shock wave solutions and thus is acausal. Ironically, this pathology arises from the very constraint that removes the (sixth) Boulware-Deser ghost mode.