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Uniqueness of the Trautman-Bondi mass

Piotr T. Chruściel*

Jacek Jezierski†

Malcolm A. H. MacCallum‡

  • Département de Mathématiques, Faculté des Sciences, Université de Tours, Parc de Grandmont, F-37200 Tours, France

  • Department of Mathematical Methods in Physics, University of Warsaw, ul. Hoża 74, 00-682 Warszawa, Poland

  • School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, United Kingdom

  • *Email address: Chrusciel@Univ-Tours.Fr
  • †Email address: jjacekj@fuw.edu.pl
  • ‡Email address: M.A.H.MacCallum@qmw.ac.uk
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Phys. Rev. D 58, 084001 – Published 28 August, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.084001

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 I, 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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Phys. Rev. D 58, 084001– Published 28 August, 1998
  • Received 6 March 1998

© 1998 American Physical Society

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