Gravitational waves in a minimal gravitational SME

In this work, we investigate the generation and propagation of gravitational waves within a minimal gravitational SME (Standard Model Extension). Starting from the modified graviton dispersion relation derived in the linearized gravity sector, we analyze the polarization properties of gravitational waves in the transverse–traceless tensor sector. We then construct the retarded Green function associated with the Lorentz–violating wave operator, explicitly verifying the causal structure of the theory and identifying the modified propagation speeds of the tensorial modes. In addition, we study the source–induced emission of gravitational waves from a binary black–hole system. We show that the gravitational waveform preserves the standard quadrupolar amplitude and polarization structure, while Lorentz–violating effects enter exclusively through a modification of the retarded time. As a result, the spatial components of the metric perturbation h ij ( t, r ) acquire a phase shift determined by the SME coefficients. Finally, we estimate phenomenological bounds to the model under consideration.