A note on teleparallel Killing vector fields in Bianchi type VIII and IX space—times in teleparallel theory of gravitation

2011 ◽  
Vol 20 (7) ◽  
pp. 070401 ◽  
Author(s):  
Ghulam Shabbir ◽  
Amjad Ali ◽  
Suhail Khan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Type Viii ◽  
Viii And Ix ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

A NOTE ON KILLING VECTOR FIELDS OF BIANCHI TYPE II SPACETIMES IN TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (20) ◽  
pp. 1733-1740 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Type Ii ◽  
Direct Integration ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

The aim of this paper is to classify Bianchi type II spacetimes according to their teleparallel Killing vector fields using the direct integration technique. Studying teleparallel Killing vector fields in the above spacetimes, it turns out that the dimensions of the teleparallel Killing vector fields are 4, 5 or 7. A brief comparison between teleparallel and general relativity Killing vector fields are given. It is shown that for the above spacetimes in the presence of torsion we get more conservation laws which are different from the theory of general relativity.

CLASSIFICATION OF CYLINDRICALLY SYMMETRIC STATIC SPACETIMES ACCORDING TO THEIR KILLING VECTOR FIELDS IN TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (07) ◽  
pp. 525-533 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Minkowski Spacetime ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Cylindrically Symmetric ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

In this paper we classify cylindrically symmetric static spacetimes according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 3, 4, 6 or 10 which are the same in numbers as in general relativity. In case of 3, 4 or 6 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of r. In the case of 10 Killing vector fields the spacetime becomes Minkowski spacetime and all the torsion components are zero. The Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. It is important to note that this classification also covers the plane symmetric static spacetimes.

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.

Proper projective symmetry in LRS Bianchi type V spacetimes

2018 ◽  
Vol 33 (13) ◽  
pp. 1850073 ◽  
Author(s):  
Ghulam Shabbir ◽  
K. S. Mahomed ◽  
F. M. Mahomed ◽  
R. J. Moitsheki
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Riemann Tensor ◽  
Direct Integration ◽  
Killing Vector Fields ◽  
Rotationally Symmetric ◽  
Projective Vector ◽  
Type V ◽  
Bianchi Type V

In this paper, we investigate proper projective vector fields of locally rotationally symmetric (LRS) Bianchi type V spacetimes using direct integration and algebraic techniques. Despite the non-degeneracy in the Riemann tensor eigenvalues, we classify proper Bianchi type V spacetimes and show that the above spacetimes do not admit proper projective vector fields. Here, in all the cases projective vector fields are Killing vector fields.

scholarly journals A note on some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes and their conformal vector fields in f(R) theory of gravity

2019 ◽  
Vol 34 (11) ◽  
pp. 1950079 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
A. H. Kara ◽  
Muhammad Ramzan
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Type Iii ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity

The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes in the [Formula: see text] theory of gravity using direct integration technique. In this study, there exist only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of the cases, conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.

scholarly journals Teleparallel conformal Killing vector fields of LRS Bianchi type V spacetimes in teleparallel gravity

2017 ◽  
Vol 14 (03) ◽  
pp. 1750043 ◽  
Author(s):  
Suhail Khan ◽  
Tahir Hussain ◽  
Gulzar Ali Khan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Teleparallel Gravity ◽  
Conformal Killing ◽  
Killing Vector Fields ◽  
Integrability Conditions ◽  
Conformal Killing Vector Fields ◽  
Type V ◽  
Bianchi Type V

The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity (GR). The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of [Formula: see text] and [Formula: see text], along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit proper teleparallel CKVF in only one case, while in remaining cases the teleparallel CKVFs reduce to teleparallel Killing vector fields (KVFs). Moreover, it is shown that the LRS Bianchi type V spacetimes do not admit any proper teleparallel homothetic vector field (HVF).

A NOTE ON CLASSIFICATION OF BIANCHI TYPE I SPACETIMES ACCORDING TO THEIR TELEPARALLEL KILLING VECTOR FIELDS

2010 ◽  
Vol 25 (01) ◽  
pp. 55-61 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Type I ◽  
Direct Integration ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Bianchi Type I

In this paper we classify Bianchi type I spacetimes according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 3, 4, 6 or 10 which are the same in numbers as in general relativity. In case of 3, 4 or 6 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 10 Killing vector fields, the spacetime becomes Minkowski and all the torsion components are zero. The Killing vector fields in this case are exactly the same as in the general relativity.

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