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.