Showing papers on "Ricci decomposition published in 1985"
TL;DR: In this paper, a geometric definition of the concept of isotropic singularity in a spacetime has been given, motivated by the ideas of quiescent cosmology and Penrose's Weyl tensor hypothesis.
Abstract: Motivated by the ideas of quiescent cosmology and Penrose's Weyl tensor hypothesis concerning the 'big bang', the authors give a geometric (and hence coordinate-independent) definition of the concept of 'isotropic singularity' in a spacetime. The definition generalises previous work on 'quasi-isotropic' and 'Friedman-like' singularities. They discuss simple consequences of the definition. In particular it is shown that an isotropic singularity is a scalar polynomial curvature singularity at which the Weyl tensor is dominated by the Ricci tensor. Finally they impose the Einstein field equations with irrotational perfect fluid source. This enables them to give a detailed description of the geometric structure of an isotropic singularity.
147 citations
TL;DR: In this paper, a tensor product for complete lattices via concept lattices is studied and a characterization as a universal solution and an ideal representation of the tensor products are given.
Abstract: A tensor product for complete lattices is studied via concept lattices. A characterization as a universal solution and an ideal representation of the tensor products are given. In a large class of concept lattices which contains all finite ones, the subdirect decompositions of a tensor product can be determined by the subdirect decompositions of its factors. As a consequence, one obtains that the tensor product of completely subdirectly irreducible concept lattices of this class is again completely subdirectly irreducible. Finally, applications to conceptual measurement are discussed.
52 citations
TL;DR: Actions for self-interacting N = 2 tensor multiplets are written as integrals over general or chiral superspace in this article, and the general form for SU(2)-invariant actions is given.
48 citations
TL;DR: In this article, a cosmological constant was used to construct a solution to Einstein's equations with two parameters, i.e., a Weyl tensor W++W-, and a Petrov type D. The authors showed that in some cases the solution is complete.
Abstract: The author constructs a solution to Einstein's equations with a cosmological constant. The metric contains two parameters (a,b). When b=0 the metric is recognized as the Eguchi-Hanson I (II) solution with anti-self-dual Weyl tensor W-. When a=0 it is seen to be the (pseudo) Fubini Study metric with a self-dual Weyl tensor W+. The solution has a Weyl tensor W++W-, is a Kahler metric, and is of Petrov type D. The author shows that in some cases the metric is complete.
38 citations
TL;DR: In this paper, the energy-momentum tensor for the thermal scalar gas in curved space-time was calculated using the effective Einstein equation at finite temperature, and the curvature effect vanishes in a conformally invariant theory up to the order of β 0 −2 in the high-temperature expansion.
29 citations
20 citations
TL;DR: This work gives explicit formulas for all components of the Riemannian connection and curvature tensor for a class of metrics which describe low-energy deformations in Kaluza-Klein theories with homogeneous fibers.
Abstract: We give explicit formulas for all components of the Riemannian connection and curvature tensor for a class of metrics which describe low-energy deformations in Kaluza-Klein theories with homogeneous fibers.
16 citations
TL;DR: In this paper, it was proved that ITPFI's of bounded type are ITP FI's 2, which answers a question asked by E. J. Woods, using Krieger's theorem.
Abstract: It is proved, using Krieger's theorem, that ITPFI's of bounded type are ITPFI 2 . This answers a question asked by E. J. Woods.
16 citations
TL;DR: Subnormal and quasinormal tensor product operators and generalized derivations on the Hilbert-Schmidt class were characterized in this article, where the generalized derivation on the class of tensor products was studied.
Abstract: Subnormal and quasinormal tensor product operators and generalized derivations on the Hilbert-Schmidt class will be characterized.
16 citations
TL;DR: In this paper, the authors present the full integrability conditions for the Penrose-Floyd equation and then proceed to the integration of the Einstein equations under the assumption of the existence of a PenroseFloyd tensor and find all space times admitting such a tensor.
Abstract: We present the full integrability conditions for the Penrose-Floyd equation. Then we proceed to the integration of the Einstein equations under the assumption of the existence of a Penrose-Floyd tensor and we find all space-times admitting such a tensor.
15 citations
TL;DR: In this article, the authors considered the case where the Weyl tensor is of Petrov typeD and the source is a perfect fluid with equation of statep =p(w), wherep andw are the energy density and pressure of the fluid, respectively.
Abstract: We consider solutions of the Einstein field equations for which the Weyl tensor is of Petrov typeD, and whose source is a perfect fluid with equation of statep=p(w), wherep andw are the energy density and pressure of the fluid, respectively. We also impose two additional restrictions which are satisfied by most of the known solutions, namely, that the fluid 4-velocityu lies in the 2-space spanned by the two repeated principal null directions of the Weyl tensor, and that the Weyl tensor has zero magnetic part relative tou. Our main result is that for this class of solutions, the equation of state satisfies eitherdp/dw=0 ordp/dw= 1, or else the solution admits three or more Killing vector fields.
TL;DR: In this article, the relative projection constant of Li (S) ® H + G L\\ (T) in L\\(S X T) is shown to be at least 3.
Abstract: (S, E,p),(T, ©, v) are finite, nonatomic measure spaces. G and H are finite-dimensional subspaces of Li(S) and L\\(T) respectively. Both G and H contain the constant functions. It is shown that the relative projection constant of Li (S) ® H + G L\\ (T) in L\\ (S X T) is at least 3.
TL;DR: In this article, the application of parity, time, charge, hermitian and quasi-spin conjugations to the set of irreducible tensor operators is discussed.
Abstract: The application of parity, time, charge, hermitian and quasi-spin conjugations to the set of irreducible tensor operators separates two classes of tensor operators: polar and axial. Various product tensor operators, in particular one- and two-body double tensor operators, are subsequently examined as to their conjugation properties. As a result, new selection rules are found for their matrix elements which emphasize the need for a more precise labelling of tensorial ranks in order to account for the polar content and enable configuration mixing effects. The derived results are of particular importance to the form of phenomenological and equivalent Hamiltonians of atomic and molecular physics which are often presented as series of double tensor operators.
01 Dec 1985
TL;DR: In this article, a condition necessaire et suffisante for the existence of metriques d'Einstein-Kahler sur des P 1 (C)-fibres sur des espaces symetriques hermitiens de type compact is defined.
Abstract: On donne des exemples de varietes d'Einstein-Kahler compactes avec premiere classe de Chein positive qui ne sont pas homogenes. On donne une condition necessaire et suffisante pour l'existence de metriques d'Einstein-Kahler sur des P 1 (C)-fibres sur des espaces symetriques hermitiens de type compact
TL;DR: In this paper, the authors formulate a simple model of the primordial scalar field theory, in which the metric tensor is a generalization of the scalar tensor from electrodynamics in a medium.
Abstract: We formulate a simple model of the “primordial” scalar field theory in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less thanc. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the “spontaneous” splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle.