No vDVZ Discontinuity in Non-Fierz-Pauli Theories

TL;DR

This paper demonstrates that non-Fierz-Pauli massive gravity theories avoid the vDVZ discontinuity by having a smooth massless limit, contrasting with the singular behavior in Fierz-Pauli theories.

Contribution

It shows that non-Fierz-Pauli theories, which are unitary non-perturbatively, do not exhibit the vDVZ discontinuity, unlike Fierz-Pauli theories, providing a new perspective on massive gravity.

Findings

Non-Fierz-Pauli theories have a smooth massless limit.

vDVZ discontinuity is an artifact of Fierz-Pauli mass term.

Perturbative discontinuity appears in constrained gravity.

Abstract

In theories of massive gravity with Fierz-Pauli mass term at the linearized level, perturbative radially symmetric asymptotic solutions are singular in the zero mass limit, hence van Dam-Veltman-Zakharov (vDVZ) discontinuity. In this note, in the context of gravitational Higgs mechanism, we argue that in non-Fierz-Pauli theories, which non-perturbatively are unitary, perturbative radially symmetric asymptotic solutions have a smooth massless limit, hence no vDVZ discontinuity. Perturbative vDVZ discontinuity as an artifact of the Fierz-Pauli mass term becomes evident in the language of constrained gravity, which is the massless limit of gravitational Higgs mechanism.