Lorentz symmetry in ghost-free massive gravity

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