Search results for " Tensor"
showing 10 items of 210 documents
On the classification of type D space–times
2002
We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-exi…
A relativistic approach to gravitational instability in the expanding Universe: second-order Lagrangian solutions
1994
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and geometric quantities and compared with the corresponding ones in the Newtonian approximation. Specifically, we compute the density, the volume expansion scalar, the shear, the ``electric" part, or tide, and the ``magnetic" part of the Weyl tensor. The evolution of the shear and the tide beyond the linear regime strongly depends on the ratio of the characteristic size of the perturbation to the cosmological horizon distance. For perturbations on sub--horizon scal…
On the algebraic types of the Bel–Robinson tensor
2008
The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov-Bel types and the additional ones are intrinsically characterized in terms of the sole Bel-Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.
Two-Perfect Fluid Interpretation of an Energy Tensor
1990
The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained.
Nonlinear evolution of cosmological inhomogeneities
2008
The nonlinear evolution of a cosmologically significant fluid is studied up to shell crossing. The magnetic part of the Weyl tensor, the pressure and the vorticity vanish. A suitable spatial grid is chosen. The relativistic Ellis equations are particularized on the world lines defined by the nodes of the grid and, then, the resulting equations are numerically solved. The integrations are performed in suitable Lagrangian inertial coordinates, in which the differential equations become ordinary. After the integration, a method to change from Lagrangian to Eulerian coordinates is applied. This approach has been outlined with the essential aim of studying the evolution of large scale cosmologic…
Tensor products, multiplications and Weyl’s theorem
2005
Tensor productsZ=T 1⊗T 2 and multiplicationsZ=L T 1 R T 2 do not inherit Weyl’s theorem from Weyl’s theorem forT 1 andT 2. Also, Weyl’s theorem does not transfer fromZ toZ*. We prove that ifT i,i=1, 2, has SVEP (=the single-valued extension property) at points in the complement of the Weyl spectrumσ w(Ti) ofT i, and if the operatorsT i are Kato type at the isolated points ofσ(Ti), thenZ andZ* satisfy Weyl’s theorem.
Ricci Tensors on Some Infinite Dimensional Lie Algebras
1999
Abstract The Ricci tensor has been computed in several infinite dimensional situations. In this work, we shall be interested in the case of the central extension of loop groups and in the asymptotic behaviour of the Ricci tensor on free loop groups as the Riemannian metric varies.
Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry
2001
Abstract We shall establish in the context of adapted differential geometry on the path space P m o ( M ) a Weitzenbock formula which generalizes that in (A. B. Cruzeiro and P. Malliavin, J. Funct. Anal . 177 (2000), 219–253), without hypothesis on the Ricci tensor. The renormalized Ricci tensor will be vanished. The connection introduced in (A. B. Cruzeiro and S. Fang, 1997, J. Funct. Anal. 143 , 400–414) will play a central role.
Etude des effets collisionnels dans les molécules tétraédriques. Applications au méthane perturbé par l'argon
1996
This thesis is devoted to the study of relaxational and collisional line-broadening processes in the first vibrational polyads of tetrahedral molecules. In a first part, the particular internal dynamics of such molecules is discussed. The second chapter reviews the literature on phenomena induced by intermolecular interactions involving this type of molecules. More theoretical aspects are developed in the second part. The so-called tetrahedral tensorial formalism adapted to the construction of Hamiltonians and transition moments of tetrahedral molecules is described. Main features of the infrared line-shapes theories and of semi-classical line-broadening and line-shifting calculations are a…
On the tensor degree of finite groups
2013
We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.