Bondi-Sachs Energy-Momentum for the CMC Initial Value Problem
James M. Bardeen, Luisa T. Buchman
TL;DR
This paper derives explicit formulas for Bondi-Sachs energy-momentum in the context of the initial value problem in general relativity on CMC hypersurfaces, providing numerical results to interpret Bowen-York solutions.
Contribution
It introduces explicit formulas for Bondi-Sachs quantities on CMC hypersurfaces and applies them to analyze Bowen-York initial data numerically.
Findings
Explicit formulas for Bondi-Sachs energy and momentum.
Numerical interpretation of Bowen-York solutions.
Analysis of asymptotic behavior near null infinity.
Abstract
The constraints on the asymptotic behavior of the conformal factor and conformal extrinsic curvature imposed by the initial value equations of general relativity on constant mean extrinsic curvature (CMC) hypersurfaces are analyzed in detail. We derive explicit formulas for the Bondi-Sachs energy and momentum in terms of coefficients of asymptotic expansions on CMC hypersurfaces near future null infinity. Precise numerical results for the Bondi-Sachs energy, momentum, and angular momentum are used to interpret physically Bowen-York solutions of the initial value equations on conformally flat CMC hypersurfaces of the type obtained earlier by Buchman et al. [Phys. Rev. D 80:084024 (2009)].
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