  Gravitational wave solutions with spontaneous Lorentz symmetry breaking are
studied. This breaking is triggered by a vector field, known as the bumblebee
field. A brief analysis of the main consequences of this symmetry breaking on
free-waves solutions and in the presence of matter sources are presented. For
the free case, the modified wave equation for the gravitational perturbation
field is solved, and we compare the polarization states with the usual
solution. Considering a current that acts as a source of the radiation, we
solve the equation of motion using the Green function method. Finally,
considering that the source has slow motion, we derive the new quadrupole
formula.
