Bondi-Sachs energy-momentum for the constant mean extrinsic curvature initial value problem

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 initial data on conformally flat CMC hypersurfaces similar to that calculated earlier by Buchman et al. [ L. T. Buchman, H. P. Pfeiffer and J. M. Bardeen Phys. Rev. D 80 084024-1 (2009)].