Jul 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978gregr...9..637d&link_type=abstract
General Relativity and Gravitation, vol. 9, July 1978, p. 637-654.
Mathematics
1
Formalism, Riemann Manifold, Dimensional Analysis, Manifolds (Mathematics)
Scientific paper
'Heaven' is defined as a four-dimensional complex manifold whose points are asymptotically shear-free cross sections ('good slices') of complexified null infinity; 'miniheaven' is a real two-dimensional Riemannian manifold which is a real subspace of the full complex heaven. A real miniheaven is constructed from the axisymmetric class of radiation fields originally treated by Bondi et al. (1962). The formalism is applied to the special miniheavens constructed from axisymmetric Robinson-Trautman (RT) spacetimes, which contain a one-parameter family of globally shear-free null hypersurfaces whose intersections with future null infinity are a one-parameter family of real good slices corresponding to a curve in miniheaven called the RT worldline. It is found that the RT worldline is a heavenly center-of-mass worldline along which the heavenly angular momenta vanish and that all heavenly supermomenta are constant along the RT worldline. A linearized analysis based on perturbation theory shows that the miniheaven has the same asymptotic-flatness properties as the original RT spacetime.
Dubisch Russell
Winicour Jeffrey
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