General formulation of the vector field equations

1968 ◽  
Vol 11 (2) ◽  
pp. 95-96
Author(s):  
G. Zh. Murzagaliev
Keyword(s):  
Vector Field ◽  
Field Equations

scholarly journals Coordinating vector field equations and diagrams with a serious game in introductory physics

2021 ◽  
Author(s):  
Pascal Klein ◽  
Nicole Burkard ◽  
Larissa Hahn ◽  
Merten Nikolay Dahlkemper ◽  
Kevin Eberle ◽  
...  
Keyword(s):  
Vector Field ◽  
Introductory Physics ◽  
Serious Game ◽  
Field Equations

EVOLUTION OF CENTRAL MOMENTS FOR A GENERAL-RELATIVISTIC BOLTZMANN EQUATION: THE CLOSURE BY ENTROPY MAXIMIZATION

2002 ◽  
Vol 14 (05) ◽  
pp. 469-510 ◽  
Author(s):  
ZBIGNIEW BANACH ◽  
WIESLAW LARECKI
Keyword(s):  
Vector Field ◽  
Boltzmann Equation ◽  
Velocity Vector ◽  
Hyperbolic Systems ◽  
Velocity Vector Field ◽  
Field Equations ◽  
Entropy Maximization ◽  
Central Moments ◽  
Relativistic Boltzmann Equation ◽  
Lorentzian Metric

Beginning from the relativistic Boltzmann equation in a curved space-time, and assuming that there exists a fiducial congruence of timelike world lines with four-velocity vector field u, it is the aim of this paper to present a systematic derivation of a hierarchy of closed systems of moment equations. These systems are found by using the closure by entropy maximization. Our concepts are primarily applied to the formalism of central moments because if an alternative and more familiar theory of covariant moments is taken into account, then the method of maximum entropy is ill-defined in a neighborhood of equilibrium states. The central moments are not covariant in the following sense: two observers looking at the same relativistic gas will, in general, extract two different sets of central moments, not related to each other by a tensorial linear transformation. After a brief review of the formalism of trace-free symmetric spacelike tensors, the differential equations for irreducible central moments are obtained and compared with those of Ellis et al. [Ann. Phys. (NY)150 (1983) 455]. We derive some auxiliary algebraic identities which involve the set of central moments and the corresponding set of Lagrange multipliers; these identities enable us to show that there is an additional balance law interpreted as the equation of balance of entropy. The above results are valid for an arbitrary choice of the Lorentzian metric g and the four-velocity vector field u. Later, the definition of u as in the well-known theory of Arnowitt, Deser, and Misner is proposed in order to construct a hierarchy of symmetric hyperbolic systems of field equations. Also, the Eckart and Landau–Lifshitz definitions of u are discussed. Specifically, it is demonstrated that they lead, in general, to the systems of nonconservative equations.

Symmetry group of generalized vector field equations

1977 ◽  
Vol 20 (8) ◽  
pp. 1021-1023
Author(s):  
V. I. Strazhev
Keyword(s):  
Vector Field ◽  
Symmetry Group ◽  
Field Equations

scholarly journals Late cosmic acceleration in a vector-Gauss–Bonnet gravity model

2016 ◽  
Vol 31 (01) ◽  
pp. 1650009 ◽  
Author(s):  
A. Oliveros ◽  
Enzo L. Solis ◽  
Mario A. Acero
Keyword(s):  
Vector Field ◽  
State Parameter ◽  
Cosmic Acceleration ◽  
Accelerated Expansion ◽  
Model Parameters ◽  
Tensor Model ◽  
Field Equations ◽  
Small Perturbations ◽  
Expansion Phase ◽  
Analytical Expressions

In this work, we study a general vector–tensor model of dark energy (DE) with a Gauss–Bonnet term coupled to a vector field and without explicit potential terms. Considering a spatially flat Friedmann–Robertson–Walker (FRW) type universe and a vector field without spatial components, the cosmological evolution is analyzed from the field equations of this model considering two sets of parameters. In this context, we have shown that it is possible to obtain an accelerated expansion phase of the universe since the equation state parameter [Formula: see text] satisfies the restriction [Formula: see text] (for suitable values of model parameters). Further, analytical expressions for the Hubble parameter [Formula: see text], equation state parameter [Formula: see text] and the invariant scalar [Formula: see text] are obtained. We also find that the square of the speed of sound is negative for all values of redshift, therefore, the model presented here shows a sign of instability under small perturbations. We finally perform an analysis using [Formula: see text] observational data and we find that for the free parameter [Formula: see text] in the interval [Formula: see text], at 99.73% C.L. (and fixing [Formula: see text] and [Formula: see text]), the model has a good fit to the data.

scholarly journals The Pfeiffer-Lax-Sato type vector field equations and the related integrable versal deformations

2016 ◽  
Vol 48 (2) ◽  
Author(s):  
D. Blackmore ◽  
A. Prykarpatski ◽  
M. Vovk ◽  
P. Pukach ◽  
Ya. Prykarpatski
Keyword(s):  
Vector Field ◽  
Field Equations ◽  
Versal Deformations

scholarly journals On axially symmetric space–times admitting homothetic vector fields in Lyra’s geometry

2016 ◽  
Vol 94 (11) ◽  
pp. 1148-1152
Author(s):  
Ragab M. Gad ◽  
A.E. Al Mazrooei
Keyword(s):  
Vector Field ◽  
Symmetric Space ◽  
Vector Fields ◽  
Displacement Vector ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Homothetic Vector ◽  
Lyra’S Geometry

This paper investigates axially symmetric space–times that admit a homothetic vector field based on Lyra’s geometry. The cases when the displacement vector is a function of t and when it is constant are studied. In the context of this geometry, we find and classify the solutions of the Einstein’s field equations for the space–time under consideration, which display a homothetic symmetry.

scholarly journals Minimum action solutions of some vector field equations

1984 ◽  
Vol 96 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Haim Brezis ◽  
Elliott H. Lieb
Keyword(s):  
Vector Field ◽  
Field Equations

scholarly journals PALATINI FORMALISM OF FIVE-DIMENSIONAL KALUZA–KLEIN THEORY

2005 ◽  
Vol 20 (05) ◽  
pp. 345-353 ◽  
Author(s):  
YOU DING ◽  
YONGGE MA ◽  
MUXIN HAN ◽  
JIANBING SHAO
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Palatini Formalism ◽  
Klein Theory ◽  
Kaluza Klein

The Einstein field equations can be derived in n dimensions (n>2) by the variations of the Palatini action. The Killing reduction of five-dimensional Palatini action is studied on the assumption that pentads and Lorentz connections are preserved by the Killing vector field. A Palatini formalism of four-dimensional action for gravity coupled to a vector field and a scalar field is obtained, which gives exactly the same field equations in Kaluza–Klein theory.

Generalized Ricci recurrent spacetimes and GRW spacetimes

2021 ◽  
pp. 2150209
Author(s):  
Sudhakar K. Chaubey ◽  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Almost Ricci Soliton ◽  
Perfect Fluid Spacetime ◽  
Fluid Spacetimes

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An [Formula: see text]-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)n GRW spacetime is Einstein. The properties of (GR)n GRW spacetimes equipped with almost Ricci soliton are studied.

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