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The positivity of the Bondi mass has been proven in 4 dimensions, but inhigher dimensions the issue remains open. The formalism of the present paperhas been developed to investigate this and is well suited to the higherdimensional case. At null infinity, we make asymptotic expansions of the metriccomponents in conformal Gaussian null coordinates, and use the vacuum Einsteinequations to solve for the expansion coefficients. We find simple coordinateformulae for the Bondi mass, news and flux in terms of the expansioncoefficients of the metric components. We also make expansions of the generatorof an asymptotic symmetry and obtain expressions for its expansion coefficientsin terms of those of the metric components. We make a spinorial asymptoticexpansion of a solution to the Dirac equation in the four dimensional case, anduse it to give a clean proof that the Bondi mass is positive in fourdimensions. The generalisation to higher dimensions has been investigated, butnot yet resolved: indeed, the spinor mass appears to be divergent in the higherdimensional case, because of terms which appear to be singular in the limit atinfinity. Such apparently singular terms are common in many of ourcalculations, 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 inhigher dimensions, so further investigation is required.

Asymptotic Expansions and Bondi Positivity in Higher Dimensional Relativity