Taub numbers at future null infinity: III. The Bondi mass

Abstract

This work extends the ideas developed in two previous papers by the authors. First- and second-order perturbation solutions of Einstein's equations (in Newman - Penrose form) for the Bondi - Sachs metric are found on a background Minkowski manifold. These solutions allow a tensorial calculation of the Bondi mass using the Taub superpotential.