Bondi (1962) proved mathematically the existence of gravitational waves at null infinity. He found an exact solution of Einstein equations. Within this metric, he calculated the loss of mass due to the emission of gravitational waves. The mas of a system is constant if and only if there is no news. If there is news, the mass decreases as long as there are news.
Babiuc M. (2015, April). Gravitational & electromagnetic waves on the null cone. Slides presented at APS April Meeting 2015, Baltimore, MD.