  The role of Lorentz symmetry in ghost-free massive gravity is studied,
emphasizing features emerging in approximately Minkowski spacetime. The static
extrema and saddle points of the potential are determined and their Lorentz
properties identified. Solutions preserving Lorentz invariance and ones
breaking four of the six Lorentz generators are constructed. Locally, globally,
and absolutely stable Lorentz-invariant extrema are found to exist for certain
parameter ranges of the potential. Gravitational waves in the linearized theory
are investigated. Deviations of the fiducial metric from the Minkowski metric
are shown to lead to pentarefringence of the five wave polarizations, which can
include superluminal modes and subluminal modes with negative energies in
certain observer frames. The Newton limit of ghost-free massive gravity is
explored. The propagator is constructed and used to obtain the gravitational
potential energy between two point masses. The result extends the Fierz-Pauli
limit to include corrections generically breaking both rotation and boost
invariance.
