A note on classification of locally rotationally symmetric Bianchi type I space-times via conformal vector fields in f(T,B) gravity

This paper aims to investigate Conformal Vector Fields (CVFs) of Bianchi type-I spacetimes. A set of 10-coupled Partial Differential Equations (PDEs) is obtained from the conformal Killing equations. These equations are solved by using direct integration techniques to explore the components of CVFs. Utilizing these components, we get a system of three integrability conditions. Finally, we achieve CVFs along with conformal factors for unique possibilities of unknown metric functions from the solution of these conditions. From our results, it is examined that Bianchi type-I spacetimes admit five or fifteen CVFs for specific choices of metric functions.

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Existence of conformal vector fields of Bianchi type I space-times in f(R) gravity

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820501133 ◽

2020 ◽

Vol 17 (08) ◽

pp. 2050113 ◽

Cited By ~ 2

Author(s):

Ghulam Shabbir ◽

Fiaz Hussain ◽

S. Jamal ◽

Muhammad Ramzan

Keyword(s):

Vector Fields ◽

Bianchi Type ◽

Flat Space ◽

Type I ◽

Direct Integration ◽

Conformally Flat ◽

Bianchi Type I ◽

Conformal Vector ◽

Conformal Vector Fields ◽

Integration Techniques

In this paper, Bianchi type I space-times in the [Formula: see text] theory of gravity are classified via conformal vector fields using algebraic and direct integration techniques. In this classification, we show that the conformal vector fields are of dimension four, five, six or fifteen. Additionally, we found that non-conformally flat Bianchi type I space-times admit conformal vector fields of dimension four, five or six. In the case of conformally flat or flat space-times, the dimension of the conformal vector fields is fifteen.

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On symmetries and conservation laws of some spacetimes in f(R, T) gravity

Modern Physics Letters A ◽

10.1142/s0217732319750038 ◽

2019 ◽

Vol 34 (36) ◽

pp. 1975003

Author(s):

Ashfaque H. Bokhari ◽

A. H. Kara ◽

B. Gadjagboui

Keyword(s):

Conservation Laws ◽

Detailed Analysis ◽

Bianchi Type ◽

Type I ◽

Noether’S Theorem ◽

Bianchi Type I ◽

Plane Symmetric ◽

Locally Rotationally Symmetric ◽

Rotationally Symmetric ◽

Variational Symmetries

We undertake a detailed analysis of the symmetry structures of the plane symmetric and the locally rotationally symmetric (LRS) Bianchi type I spacetimes in the [Formula: see text] gravity. In particular, we construct all the variational symmetries associated with its Lagrangian and, in some cases, construct the associated conservation laws using Noether’s theorem. Giving a comparison between isometries and variational symmetries, we give symmetry structures of some well-known spacetimes.

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Locally rotationally symmetric Bianchi type I cosmology in f(R, T) gravity

The European Physical Journal C ◽

10.1140/epjc/s10052-015-3582-7 ◽

2015 ◽

Vol 75 (8) ◽

Cited By ~ 77

Author(s):

M. Farasat Shamir

Keyword(s):

Bianchi Type ◽

Type I ◽

Bianchi Type I ◽

Locally Rotationally Symmetric ◽

Rotationally Symmetric

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VISUALIZING MINISUPERSPACE DYNAMICS

Modern Physics Letters A ◽

10.1142/s0217732393003202 ◽

1993 ◽

Vol 08 (30) ◽

pp. 2815-2825 ◽

Cited By ~ 2

Author(s):

KJELL ROSQUIST ◽

CLAES UGGLA

Keyword(s):

Bianchi Type ◽

Type I ◽

Bianchi Type I ◽

Locally Rotationally Symmetric ◽

Rotationally Symmetric

We show that one can find a useful compactified representation of minisuperspace dynamics using conformal diagrams and how global and asymptotic qualitative features of the dynamics can be inferred from. the diagrams. To provide explicit examples this is done for the locally rotationally symmetric Bianchi type I and IX models.

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

Modern Physics Letters A ◽

10.1142/s0217732310033189 ◽

2010 ◽

Vol 25 (25) ◽

pp. 2145-2153 ◽

Cited By ~ 9

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.

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