Uniqueness of the Trautman-Bondi mass

It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth "piece'' of conformal null infinity T, are those depending on the metric only through a specific combination of the Bondi "mass aspect'' and other next-to-leading order terms in the metric. Under the extra condition of passive EMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman-Bondi energy. It is also shown that this energy remains well defined for a wide class of ''polyhomogeneous'' metrics. [S0556-2821(98)05916-5].