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.
Highlights
Introduction and SummaryA general Lorentz invariant mass term for the graviton hMN in the linearized approximation is of the form m2 − [ hM N hM − β(hM M )2] (1)where β is a dimensionless parameter
For β = 1 perturbative radially symmetric asymptotic solutions are singular in the m → 0 limit: we have the van DamVeltman-Zakharov discontinuity [6, 7] and we must consider non-perturbative solutions [8]
In this note, following the method of [9], we argue that for β= 1 perturbative solutions have a smooth massless limit, no van Dam-Veltman-Zakharov (vDVZ) discontinuity
Summary
A general Lorentz invariant mass term for the graviton hMN in the linearized approximation is of the form m2 −. For β= 1 the trace component hM M is a propagating ghost, while it decouples in the Minkowski background for the Fierz-Pauli mass term with β = 1 [1]. Gravitational Higgs mechanism [2, 3] provides a non-perturbative and fully covariant definition of massive gravity. Non-perturbatively, even for β= 1, the Hamiltonian is bounded from below and the perturbative ghost is an artifact of linearization [4].1. The perturbative vDVZ discontinuity is an artifact of the Fierz-Pauli mass term. This becomes evident in the language of constrained gravity, which is the massless limit of gravitational Higgs mechanism [9]
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