Numerical Relativity and Asymptotic Flatness

TL;DR

This paper develops a method for numerical relativity to construct charts and tetrads near infinity, enabling the estimation of Bondi news, mass, and its decrease directly from numerical data.

Contribution

It introduces a way to bridge numerical relativity data with theoretical asymptotic concepts like Bondi news and mass loss.

Findings

Constructed asymptotic charts from numerical data

Enabled estimation of Bondi news and mass loss

Provided practical recipes for numerical relativity

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.