Physics
Scientific paper
Dec 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978phrvd..18.4399p&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 18, Dec. 15, 1978, p. 4399-4407.
Physics
2
Conservation Equations, Gravitation Theory, Kinetic Energy, Momentum Theory, Relativity, Space-Time Functions, Coordinate Transformations, Einstein Equations, Euclidean Geometry, Field Theory (Physics), Riemann Manifold, Tensors, Vector Spaces
Scientific paper
The paper attempts to give a meaningful definition of the total energy-momentum content of a spacelike three-surface of a generic space-time. This definition has the following properties: (1) it is covariant; (2) it does not depend on the choice of some preferred geometric element but does depend on the choice of a timelike world line (or observer); (3) it satisfies an integral conservation equation; (4) its generators are given in terms of a canonical mapping onto space-time of a basis of vectors in the tangent spaces to the tangent bundle; and (5) it contains a contribution (due to the radiative or 'non-Coulomb' part of the gravitational field) a component of which necessarily vanishes when space-time admits a Killing vector. It is concluded that for a topologically Euclidean region of an arbitrarily curved space-time the energy-momentum concept is valid.
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