MASS CORRECTION AND GRAVITATIONAL ENERGY RADIATION IN BLACK-HOLE PERTURBATION-THEORY

Using second-order black-hole perturbation theory, we show that the di fference between the ADM mass and the final black-hole mass, computed to the lowest significant order, is equal, to the same order, to the t otal gravitational radiation energy, obtained by applying the Landau-L ifschitz (pseudotensor) equation to the first-order perturbation. This result may be considered as a consistency check for the theory.