  Massive gravity (mGR) describes a dynamical "metric" on a fiducial,
background one. We investigate fluctuations of the dynamics about mGR
solutions, that is about its "mean field theory". Analyzing mean field massive
gravity propagation characteristics is not only equivalent to studying those of
the full non-linear theory, but also in direct correspondence with earlier
analyses of charged higher spin systems, the oldest example being the charged,
massive spin 3/2 Rarita--Schwinger (RS) theory. The fiducial and mGR mean field
background metrics in the mean field mGR model correspond to the RS Minkowski
metric and external EM field. The common implications in both systems are that
hyperbolicity holds only in a weak background-mean-field limit, immediately
ruling both theories out as fundamental theories. Although both can still be
considered as predictive effective models in the weak regime, their lower
helicities exhibit superluminal behavior: lower helicity gravitons are
superluminal as compared to photons propagating on either the fiducial or
background metric. This "crystal-like" phenomenon of differing helicities
having differing propagation speeds in both mean field mGR and mGR is a
peculiar feature of these models.

High Energy Physics - Theory;General Relativity and Quantum Cosmology