Physics
Scientific paper
Feb 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980gregr..12..149p&link_type=abstract
General Relativity and Gravitation, vol. 12, Feb. 1980, p. 149-154.
Physics
5
Energy, Gravitational Waves, Momentum, Relativity, Space-Time Functions, Coordinate Transformations, Field Theory (Physics), Gravitation Theory, Scalars, Tensor Analysis
Scientific paper
By using a suitable two-point scalar field, a covariant formulation of the Einstein pseudotensor is given. A unique choice of scalar field is made possible by examining the role of linear and angular momentum in their correct geometric context. It is shown that, contrary to many text-book statements, linear momentum is not generated by infinitesimal coordinate transformations on space-time. Use is made of the nonintersecting lifted geodesics on the tangent bundle, to space-time, to define a globally regular three-dimensional Lagrangian submanifold of the tangent bundle, relative to an observer at some point z in space-time. By integrating over this submanifold rather than a necessarily singular spacelike hypersurface, gravitational linear and angular momentum, relative to z, are defined, and shown to have sensible physical properties.
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