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Uniqueness of the Trautman--Bondi mass

Piotr T. Chruściel·Jacek Jezierski·Malcolm A. H. MacCallum
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Abstract

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 Scri, 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 BMS 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.

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Piotr T. Chruściel, Jacek Jezierski, Malcolm A. H. MacCallum. 1998-03-02. Uniqueness of the Trautman--Bondi mass. https://doi.org/10.1103/physrevd.58.084001

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