Showing papers on "Ricci decomposition published in 1986"
67 citations
TL;DR: In this paper, the authors evaluate the corrections to the usual linear relation between the scalar curvature and the trace of the energy-momentum tensor, R approximately T, replacing the usual Einstein-Hilbert Lagrangian R by an unknown function f(R) and imposing the inflationary solution upon the scale factor a(t) of the Robertson-Walker metric.
Abstract: The inflationary model proposed by Guth (1981), is based on non-classical behaviour of the energy-momentum tensor. The authors try to evaluate the corrections to the usual linear relation between the scalar curvature and the trace of the energy-momentum tensor, R approximately T, replacing the usual Einstein-Hilbert Lagrangian R by an unknown function f(R) and imposing the inflationary solution upon the scale factor a(t) of the Robertson-Walker metric. Solving for f(R) enables one to evaluate the corrections to the relation R approximately T, which may be developed in powers of R or T at will.
51 citations
TL;DR: In this paper, the authors investigated the Einstein equation for a class of (4n+4)-dimensional SU(2)-invariant metrics on S4 and R4 fiber bundles over quaternionic Kahler base manifolds.
Abstract: The authors investigate the Einstein equation for a class of (4n+4)-dimensional SU(2)-invariant metrics on S4 and R4 fibre bundles over quaternionic Kahler base manifolds. Using numerical techniques, they establish the existence of complete compact inhomogeneous Einstein spaces of this form with positive Ricci curvature, and complete non-compact inhomogeneous Einstein spaces with zero or negative Ricci curvature.
44 citations
TL;DR: There is a unique Lagrangian quadratic in the curvature tensor which yields second-order field equations in dimensions greater than four as discussed by the authors, which is applied to a Kaluza-Klein theory.
Abstract: There is a unique Lagrangian quadratic in the curvature tensor which yields second-order field equations in dimensions greater than four. This Lagrangian is applied to a Kaluza-Klein theory and its cosmological implications are investigated.
44 citations
TL;DR: In this article, a method for calculating the curvature tensor was developed and applied to the Scharzschild case, which employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
Abstract: A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
30 citations
28 citations
TL;DR: The relation between Regge's equations of motion for a simplicial manifold and the distributional Einstein tensor of the manifold is discussed in this article, where it is shown that the average of contributions to the tensor on a suitably defined 3-surface can be computed.
Abstract: The relation between Regge's equations of motion for a simplicial manifold and the distributional Einstein tensor of the manifold is discussed. Regge's equations imply that the distributional Einstein tensor vanishes 'on average', the averaging involving integrating contributions to the Einstein tensor on a suitably defined 3-surface.
9 citations
5 citations
4 citations
TL;DR: In this article, the components of the Weyl and Ricci tensors and the spin coefficients of the Plebanski metric were analyzed by means of the Newman-Penrose formalism.
Abstract: The Plebanski metric is analyzed by means of the Newman-Penrose formalism. The components of the Weyl and Ricci tensors and the spin coefficients are calculated. These results are applied to obtain the equations of gravitational perturbations around the Plebanski metric.
1 citations
TL;DR: The metric and contorsion tensors are constructed which yield a combined Riemann curvature tensor of the form R ± μνστ = ( 1 2 a 2 )(g μσ g ντ − g μτ g δ νσ ± √g ϵ μπστ ) .
Journal Article•
TL;DR: In this article, the multiplicity structure of irreducible representations of a compact semisimple Lie group is investigated for U(3, U(4) and general U(n).
Abstract: For pt.I see ibid., vol.19, p.1523 (1986). Methods introduced in previously (Edwards et al. 1986) for resolving the multiplicity of irreducible subrepresentations occurring in the decomposition of the tensor product of two irreducible representations of a compact semisimple Lie group are illustrated by application to U(3), U(4) and general U(n). For U(3) the authors rederives very simple the known multiplicity structure for an irreducible tensor operator of fixed shift weight in terms of the decomposition of tensor product highest weight vectors into certain direct product states. The use the method to illustrate structural parallels between the Clebsch-Gordan problem for general U(n) and the U(3) case, Finally, they study in detail the multiplicity structure for a specific U(4) irreducible operator showing both the similarities and differences with U(3).