UNIQUENESS OF THE TRAUTMAN-BONDI MASS - ART. NO. 084001

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