Showing papers on "Four-tensor published in 1984"

Is the Riemann tensor derivable from a tensor potential

Abstract: In recent years, following an earlier result of C. Lanczos concerning the representation of the Weyl tensor in arbitrary space-times, it has been conjectured that the Riemann tensor itself admits a linear representation in terms of the covariant derivatives of a suitable “potential” tensor of rank 3. This conjecture is shown to be false, at least for a class of spacetime geometries including several physically significant ones.

Truesdell invariance in relativistic electromagnetic fields

Abstract: The Truesdell derivative of a contravariant tensor fieldXabis defined with respect to a null congruencelaanalogous to the Truesdell stress rate in classical continuum mechanics. The dynamical consequences of the Truesdell invariance with respect to a timelike vectoruaof the stress-energy tensor characterizing a charged perfect fluid with null conductivity are the conservation of pressure (p), charged density (e) an expansion-free flow, constancy of the Maxwell scalars, and vanishing spin coefficientsα+¯β = ¯σ − λ = τ = 0 (assuming freedom conditionsk = λ = e ψ + ¯γ = 0). The electromagnetic energy momentum tensor for the special subcases of Ruse-Synge classification for typesA andB are described in terms of the spin coefficients introduced by Newman-Penrose.

Weyl kinematical groups of electromagnetic and energy-momentum tensors

Abstract: We determine the “kinematical” groups of electromagnetic fields F with respect to Weyl transformations. We find different structures for parallel and perpendicular (constant and uniform) fields. We compare the results with those obtained in the Poincare context. As a physical application, we consider the invariance conditions on associated energy-momentum tensors and get meaningful results in connection with the description of zero rest mass particles.

Spinning Fluid Energy‐Momentum Tensors in the Einstein‐Cartan Theory

Abstract: A Eulerian variational principle for a perfect fluid in general relativity was presented some years ago.’ Recently we have generalized this variational principle to deal with fluids having intrinsic s p h 2 Recent papers by Bailey and Israel also deal with spinning fluids in general relativity using a different These papers by Bailey and Israel may be consulted for earlier references to this subject. It is thought that the spin of “particles,” protogalaxies, turbulent eddies, or primeval black holes could play an important role in the dynamics of the early universe.’-’ Israel, in a brief study, found a solution for a spinning fluid in an anisotropic (Bianchi I) cosmological model.4 In this example the spin induces a Lense-Thirring rotation of the local inertial axis relative to the directions along the spin of the fluid. Further such studies should be carried out to determine how spin can affect the dynamics of the early universe. The general relativistic energy-momentum tensor for a spinning fluid derived in Reference 2 would be an appropriate starting point for such studies. Our main goal in this paper is to generalize our spinning fluid variational principle of Reference 2 to the Einstein-Cartan (EC) theory. In the EC theory spin takes on an important role as the source of the torsion part of the gravitational field. Thus, what we derive in this paper is a fundamental theory, based on a Lagrangian, which introduces spin into the EC theory for a macroscopic spinning fluid. The torsion-spin equation of our theory leads to the Weyssenhoff convective form for the canonical spin tensor, and the energy-momentum tensor has explicit spin-dependent terms. There have been several recent studies of spinning matter in the EC however, none of these studies deduces the field equations of the theory from a Eulerian variational principle such as in this paper. The theories that we studied in Reference 2 and in this paper are based on the work of Halbwachs, who formulated a Eulerian variational principle for a spinning fluid in special relativity.’ Reference 1 is a generalization of Halbwachs’ theory to general relativity for fluids without intrinsic spin, while Reference 2 is for fluids with intrinsic spin .