  The positivity of the Bondi mass has been proven in 4 dimensions, but in
higher dimensions the issue remains open. The formalism of the present paper
has been developed to investigate this and is well suited to the higher
dimensional case. At null infinity, we make asymptotic expansions of the metric
components in conformal Gaussian null coordinates, and use the vacuum Einstein
equations to solve for the expansion coefficients. We find simple coordinate
formulae for the Bondi mass, news and flux in terms of the expansion
coefficients of the metric components. We also make expansions of the generator
of an asymptotic symmetry and obtain expressions for its expansion coefficients
in terms of those of the metric components. We make a spinorial asymptotic
expansion of a solution to the Dirac equation in the four dimensional case, and
use it to give a clean proof that the Bondi mass is positive in four
dimensions. The generalisation to higher dimensions has been investigated, but
not yet resolved: indeed, the spinor mass appears to be divergent in the higher
dimensional case, because of terms which appear to be singular in the limit at
infinity. Such apparently singular terms are common in many of our
calculations, but can generally be shown to be zero before the limit is taken.
However, it is not yet clear this can be done in the case of the spinor mass in
higher dimensions, so further investigation is required.
