Lorentz transformation of three dimensional gravitational wave tensor

Abstract Recently there are more and interest on the gravitational wave of moving sources. This introduces a Lorentz transformation problem wave. Although Bondi-Metzner-Sachs (BMS) theory has in principle already included wave, three dimensional tensor not been explicitly calculated before. Within four spacetime, have property `boost weight zero' `spin 2'. fact makes difficult to understand. In current paper we adopt traditional description Such transverse-traceless describes freedom directly. We derive explicit tensor. The is similar for electric field vector magnetic which vectors. Based deduced tensor, can construct waveform source with high speed if only corresponding rest given.