Extrinsic curvature for the two-black-hole problem (Q2266246)

The solutions of the momentum constraints on the Einstein-Rosen manifold with two bridges, representing two black holes, are analyzed. These solutions are in the form of an infinite series. Their higher order terms are shown to fall off as \(r^{-6}\). These terms add multipole moments and gravitational radiation to the initial data and do not contribute to the linear and (spin) angular momenta of the black holes.