Predictability of weather and climate

Abstract:

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 geodesies on the tangent bundle, TM, to space-time, to define a globally regular three-dimensional Lagrangian submanifold of TM, 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. © 1980 Plenum Publishing Corporation.