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A simple expression for the ADM mass

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Abstract

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by David Brown and York (Phys. Rev. D 55, 1977–1984 1997; Phys. Rev. D 47, 1407–1419 1993). We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.

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  1. School of Mathematical Sciences, Monash University, Clayton Campus, Australia

    Leo Brewin

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  1. Leo Brewin
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Correspondence to Leo Brewin.

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Brewin, L. A simple expression for the ADM mass. Gen Relativ Gravit 39, 521–528 (2007). https://doi.org/10.1007/s10714-007-0403-9

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  • DOI: https://doi.org/10.1007/s10714-007-0403-9

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