Modification in Gravitational Waves Production Triggered by Spontaneous Lorentz Violation

In this work, we search how the production of gravitational waves is corrected by a spontaneous Lorentz violation triggered by the vacuum expectation value (VEV) of the bumblebee vector field (bμ ). We consider the modified graviton equations of motion by the dynamics of the bumblebee field. In this formulation the graviton is still non-massive and has two degrees of freedom, but does not has a gauge transformation and the dispersion relation changes from p2 = 0 to p2 + ξ (bμ pμ) = 0. Then, we solve these equations considering a current that acts as a source of the radiation. In this case, we apply the method of the Green’s function to find a modified quadrupole formula for the perturbation.