Numerical Relativity and Asymptotic Flatness

Abstract

It is highly plausible that the region of space-time far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al. (1962), Sachs (1962) and Newman & Unti (1962), rely on careful, clever, a-priori choices of chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap. Starting from data available in a typical numerical evolution, we construct a chart and tetrad which is, asymptotically, sufficiently close to the theoretical ones, so that the key concepts of Bondi news function, Bondi mass and its rate of decrease can be estimated. In particular these esimates can be expressed in the numerical relativist's chart as numerical relativity recipes.

24 pages, to be published in Classical and Quantum Gravity

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