The Conservation Law and the Radiation of General Relativity

This paper presents the conservation law of Einstein's General Relativity, in whichthe continuity equation of matter and gravitational field is implicitly derived from theequation of motion of matter. Although the obtained energy-momentum tensor is thesame as the Landau-Lifshitz pseudotensor. the physical and conceptual foundation aredifferent. Two alternative methods to obtain the gravitational radiation are proposed inthis paper as well The radiation will be derived from the equation of motion of matterand geodesic equation separately.