Homothetic vector fields of LRS Bianchi type-I spacetimes via the RIF tree approach

2021 ◽  
Vol 209 (3) ◽  
pp. 1673-1682
Author(s):  
U. Nasib ◽  
T. Hussain ◽  
A. H. Bokhari
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Tree Approach

scholarly journals Proper Homothetic Vector Fields of Bianchi Type I Spacetimes via Rif Tree Approach

2021 ◽  
pp. 104299
Author(s):  
Ashfaque H. Bokhari ◽  
Tahir Hussain ◽  
Jamshed Khan ◽  
Uzma Nasib
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Tree Approach

Homothetic vector fields in a specially homogenous Bianchi type-I cosmological model in Lyra geometry

2015 ◽  
Vol 93 (11) ◽  
pp. 1397-1401 ◽  
Author(s):  
A.S. Alofi ◽  
Ragab M. Gad
Keyword(s):  
Cosmological Model ◽  
Riemannian Geometry ◽  
Vector Fields ◽  
Bianchi Type ◽  
Displacement Vector ◽  
Lyra Geometry ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Vector Formula

In this paper, homothetic vector fields of a spatially homogenous Bianchi type-I cosmological model have been evaluated based on Lyra geometry. Further, we investigate the equation of state in cases when a displacement vector [Formula: see text] is a function of t and when it is constant. We give a comparison between the obtained results, using Lyra geometry, and those obtained previously in the context of general relativity, based on Riemannian geometry.

CLASSIFICATION OF BIANCHI TYPE I SPACETIMES ACCORDING TO THEIR PROPER TELEPARALLEL HOMOTHETIC VECTOR FIELDS IN THE TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (25) ◽  
pp. 2145-2153 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Special Choice ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

In this paper we explored teleparallel homothetic vector fields in Bianchi type I spacetimes in the teleparallel theory of gravitation using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11 which are same in numbers as in general relativity. In the cases of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice of the spacetimes. In the case of 11 teleparallel homothetic vector fields all the torsion components are zero. The homothetic vector fields of general relativity are recovered in this case and the spacetime become Minkowski.

Killing vector fields of Bianchi type I spacetimes via Rif tree approach

2021 ◽  
pp. 2150208
Author(s):  
Ashfaque H. Bokhari ◽  
Tahir Hussain ◽  
Wajid Hussain ◽  
Fawad Khan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Type I ◽  
Killing Vector Fields ◽  
New Approach ◽  
Bianchi Type I ◽  
Rotationally Symmetric ◽  
Metric Functions ◽  
Tree Approach

In this paper, we have adopted a new approach to study the Killing vector fields of locally rotationally symmetric and general Bianchi type I spacetimes. Instead of directly integrating the set of Killing’s equations, an algorithm is developed in Maple which converts these equations to the reduced involutive form (Rif) and consequently it imposes some restrictions on the metric functions in the form of a tree, known as Rif tree. The set of Killing’s equations is then solved for each branch of the Rif tree, giving the explicit form of the Killing vector fields. The structure of Lie algebra is presented for each set of the obtained Killing vector fields and some physical implications of the obtained metrics are discussed.

Noether symmetries of Bianchi type I spacetimes via Rif tree approach

2021 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Muhammad Farhan ◽  
Tahir Hussain
Keyword(s):  
Bianchi Type ◽  
Noether Symmetry ◽  
Type I ◽  
Noether Symmetries ◽  
Bianchi Type I ◽  
Tree Approach ◽  
Symmetry Algebras

In this paper, we have studied Noether symmetries of the general Bianchi type I spacetimes. The Lagrangian associated with the most general Bianchi type I metric is used to find the set of Noether symmetry equations. These equations are analyzed using an algorithm, developed in Maple, to get all possible Bianchi type I metrics admitting different Noether symmetries. The set of Noether symmetry equations is then solved for each metric to obtain the Noether symmetry algebras of dimensions 4, 5, 6 and 9.

Homothetic vector field in plane symmetric Bianchi type-I cosmological model in Lyra geometry

2014 ◽  
Vol 29 (22) ◽  
pp. 1450116 ◽  
Author(s):  
Ragab M. Gad ◽  
A. S. Alofi
Keyword(s):  
General Relativity ◽  
Vector Field ◽  
Riemannian Geometry ◽  
Bianchi Type ◽  
Displacement Vector ◽  
Lyra Geometry ◽  
Type I ◽  
Bianchi Type I ◽  
Plane Symmetric ◽  
Homothetic Vector

In this paper, we obtain a homothetic vector field of a plane symmetric Bianchi type-I spacetime based on Lyra geometry. We discuss the cases when the displacement vector is function of t and when it is constant. We investigate the equation of state in both two cases. A comparison between the obtained results, using Lyra geometry, and that have obtained previously in the context of General Relativity (GR), based on Riemannian geometry, will be given.

scholarly journals Homothetic Motion in a Bianchi Type –V Model in Lyra Geometry

2017 ◽  
Vol 1 (4) ◽  
Author(s):  
F. El-Sabbagh  - R. M. Gad, F. Abd.El-Bsseer, H. H. Moustafa
Keyword(s):  
Vector Field ◽  
Equation Of State ◽  
Bianchi Type ◽  
Displacement Vector ◽  
Lyra Geometry ◽  
Type I ◽  
Bianchi Type I ◽  
Homothetic Vector ◽  
Type V ◽  
Bianchi Type V

In this paper we study a homothetic vector field of a Bianchi type-V model based on Lyra geometry. The aim of this paper is to get the components of  homothetic vector field  in Lyra geometry for Bianchi type-V, compare between it and the case of  Bianchi type-I. Using ordinary method and Computer program to get the components of  the vector . The results are compatible in the two methods and get the condition that the results  tends to the case of  Bianchi type-I.  The cases when a displacement vector is a function of  t and when it is constant are considered. In both two cases we investigate the equation of state.

Concircular vector fields on Lorentzian manifold of Bianchi type-I spacetimes

2018 ◽  
Vol 33 (12) ◽  
pp. 1850063
Author(s):  
Amjad Mahmood ◽  
Ahmad T. Ali ◽  
Suhail Khan
Keyword(s):  
Differential Equations ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Lorentzian Manifold ◽  
Conformal Killing ◽  
Type I ◽  
Bianchi Type I ◽  
Conformal Killing Vector Fields ◽  
Metric Functions

Our aim in this paper is to obtain concircular vector fields (CVFs) on the Lorentzian manifold of Bianchi type-I spacetimes. For this purpose, two different sets of coupled partial differential equations comprising ten equations each are obtained. The first ten equations, known as conformal Killing equations are solved completely and components of conformal Killing vector fields (CKVFs) are obtained in different possible cases. These CKVFs are then substituted into second set of ten differential equations to obtain CVFs. It comes out that Bianchi type-I spacetimes admit four-, five-, six-, seven- or 15-dimensional CVFs for particular choices of the metric functions. In many cases, the CKVFs of a particular metric are same as CVFs while there exists few cases where proper CKVFs are not CVFs.

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