Bondi-Sachs Energy-Momentum for the CMC Initial Value Problem

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)].

version to be published in Phys. Rev. D

References in corpus (7)

• Binary-black-hole initial data with nearly-extremal spins
• An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
• Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
• Regularity of the Einstein Equations at Future Null Infinity
• Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
• Black hole initial data on hyperboloidal slices
• Hyperboloidal evolution of test fields in three spatial dimensions

Cited by in corpus (8)

• An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
• Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
• Spherically symmetric black hole spacetimes on hyperboloidal slices
• Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces
• Axisymmetric constant mean curvature slices in the Kerr space-time
• Hyperboloidal initial data without logarithmic singularities
• Plane fronted electromagnetic waves and an asymptotic limit of Liénard--Wiechert fields
• Numerical and analytical methods for asymptotically flat spacetimes