Massive Gravity Acausality Redux

TL;DR

Massive gravity theories aiming to extend GR with a finite-range graviton (five DoF) face deep consistency problems: first-order shock analyses reveal a field-dependent characteristic matrix whose zeros imply superluminal propagation, and prior second-order analyses show tachyonic modes across viable mass terms. By reformulating mGR in a Palatini, vierbein-based first-order form and deriving the relevant vector and scalar constraints, the authors compute a compact expression for the characteristic determinant and demonstrate that its vanishing is possible for reasonable field configurations, including flat fiducial backgrounds that can yield acausal, CTC-like structures. To illustrate the mechanism and reconcile different notions of superluminality, a simple two-field toy model is analyzed, showing how both first- and second-order analyses capture distinct, pathological aspects of the dynamics. Collectively, the results argue that the standard nonlinear massive gravity frameworks are unphysical within their domain of validity, and that recovering GR's consistency would require substantial structural changes or embeddings beyond the current constructions. This work thus reinforces the view that general relativity’s nonlinear structure remains uniquely robust among candidate modifications of gravity.

Abstract

Massive gravity (mGR) is a 5(=2s+1) degree of freedom, finite range extension of GR. However, amongst other problems, it is plagued by superluminal propagation, first uncovered via a second order shock analysis. First order mGR shock structures have also been studied, but the existence of superluminal propagation in that context was left open. We present here a concordance of these methods, by an explicit (first order) characteristic matrix computation, which confirms mGR's superluminal propagation as well as acausality.