A note on proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in f(R, T) theory of gravity

2019 ◽  
Vol 34 (24) ◽  
pp. 1950189 ◽  
Author(s):  
M. Jamil Khan ◽  
Ghulam Shabbir ◽  
M. Ramzan
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Killing Vector ◽  
The Other ◽  
Direct Integration ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Homothetic Vector ◽  
Theory Of Gravity

The purpose of this paper is to find proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in the [Formula: see text] theory of gravity by using direct integration technique. In this study, there exist six cases. Studying each case in detail, we found that in four cases proper homothetic vector fields exist while in the other two cases homothetic vector fields become 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.

A note on some Bianchi type II spacetimes and their conformal vector fields in f(R) theory of gravity

2019 ◽  
Vol 34 (38) ◽  
pp. 1950320 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
S. Jamal ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Type Ii ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Homothetic Vector ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity

The aim of this paper is to find proper conformal vector fields of some Bianchi type II spacetimes in the f[Formula: see text](R[Formula: see text]) theory of gravity using direct integration technique. In this study, seven cases have been discussed. Studying each case in detail, it is shown that the spacetimes under consideration do not admit proper conformal vector fields. Conformal vector fields are either homothetic vector fields or Killing vector fields.

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.

Dust static plane symmetric solutions and their conformal vector fields in f(R) theory of gravity

2018 ◽  
Vol 33 (37) ◽  
pp. 1850222 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
F. M. Mahomed ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Conformally Flat ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity ◽  
Static Plane

We first find the dust solutions of static plane symmetric spacetimes in the theory of f(R) gravity. Then using the direct integration technique on the solutions obtained, we deduce the conformal vector fields. This is performed in the context of f(R) theory of gravity. There exist six cases. Out of these, in five cases the spacetimes become conformally flat and admit 15 conformal vector fields, whereas in the sixth case, conformal vector fields become Killing vector fields.

scholarly journals Conformal and Disformal Structure of 3D Circularly Symmetric Static Metric in f(R) Theory of Gravity

2020 ◽  
Vol 39 (1) ◽  
pp. 111-116
Author(s):  
Muhammad Ramzan ◽  
Murtaza Ali ◽  
Fiaz Hussain
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Conformal Killing ◽  
Field Equations ◽  
Killing Vector Fields ◽  
Homothetic Vector ◽  
First Case ◽  
Conformal Vector Fields ◽  
Theory Of Gravity

Conformal vector fields are treated as generalization of homothetic vector fields while disformal vector fields are defined through disformal transformations which are generalization of conformal transformations, therefore it is important to study conformal and disformal vector fields. In this paper, conformal and disformal structure of 3D (Three Dimensional) circularly symmetric static metric is discussed in the framework of f(R) theory of gravity. The purpose of this paper is twofold. Firstly, we have found some dust matter solutions of EFEs (Einstein Field Equations) by considering 3D circularly symmetric static metric in the f(R) theory of gravity. Secondly, we have found CKVFs (Conformal Killing Vector Fields) and DKVFs (Disformal Killing Vector Fields) of the obtained solutions by means of some algebraic and direct integration techniques. A metric version of f(R) theory of gravity is used to explore the solutions and dust matter as a source of energy momentum tensor. This study reveals that no proper DVFs exists. Here, DVFs for the solutions under consideration are either HVFs (Homothetic Vector Fields) or KVFs (Killing Vector Fields) in the f(R) theory of gravity. In this study, two cases have been discussed. In the first case, both CKVFs and DKVFs become HVFs with dimension three. In the second case, there exists two subcases. In the first subcase, DKVFs become HVFs with dimension seven. In the second subcase, CKVFs and DKVFs become KVFs having dimension four.

A note on classification of static plane symmetric perfect fluid space-times via proper conformal vector fields in f(G) theory of gravity

2020 ◽  
Vol 17 (06) ◽  
pp. 2050086 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
M. Ramzan ◽  
Shabeela Malik ◽  
F. M. Mahomed
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Direct Integration ◽  
Conformally Flat ◽  
Plane Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity ◽  
Static Plane

In the [Formula: see text] theory of gravity, we classify static plane symmetric perfect fluid space-times via proper conformal vector fields (CVFs) using algebraic and direct integration approaches. During this classification, we found eight cases. Studying each case in detail, we found that the dimensions of CVFs are 4, 5, 6 or 15. In the cases when the space-time admits 15 independent CVFs it becomes conformally flat.

Classification of static spherically symmetric space-times in f(R) theory of gravity according to their conformal vector fields

2018 ◽  
Vol 15 (11) ◽  
pp. 1850193 ◽  
Author(s):  
Ghulam Shabbir ◽  
Muhammad Ramzan ◽  
Fiaz Hussain ◽  
S. Jamal
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Homothetic Vector ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity

A classification of static spherically symmetric space-times in [Formula: see text] theory of gravity according to their conformal vector fields (CVFs) is presented. For this analysis, a direct integration technique is used. This study reveals that for static spherically symmetric space-times in [Formula: see text] theory of gravity, CVFs are just Killing vector fields (KVFs) or homothetic vector fields (HVFs). For this classification, six cases have been discussed out of which there exists only one case for which CVFs become HVFs while in the rest of the cases CVFs become KVFs.

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.

A note on teleparallel conformal Killing vector fields in plane symmetric non-static spacetimes

2016 ◽  
Vol 13 (03) ◽  
pp. 1650030 ◽  
Author(s):  
Suhail Khan ◽  
Tahir Hussain ◽  
Gulzar Ali Khan
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Conformal Factor ◽  
Conformal Killing ◽  
Conformal Killing Vector ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Integrability Conditions ◽  
Conformal Killing Vector Fields ◽  
Metric Functions

The aim of this paper is to investigate teleparallel conformal Killing vector fields (CKVFs) in plane symmetric non-static spacetimes. Ten teleparallel conformal Killing’s equations are obtained which are linear in the components of the teleparallel CKVF [Formula: see text]. A general solution of these equations comprising the components of CKVF and conformal factor is presented, which subject to some integrability conditions. For seven particular choices of the metric functions, the integrability conditions are completely solved to get the final form of teleparallel CKVFs and conformal factor. In four different cases we get proper CKVFs, while in the remaining three cases it is shown that teleparallel CKVFs reduce to teleparallel homothetic or teleparallel Killing vector fields.

PROPER PROJECTIVE SYMMETRY IN THE SCHWARZSCHILD METRIC

2006 ◽  
Vol 21 (23) ◽  
pp. 1795-1802 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Direct Integration ◽  
Killing Vector Fields ◽  
Schwarzschild Metric ◽  
Integration Techniques ◽  
Projective Collineations

A study of proper projective symmetry in the Schwarzschild metric is given by using algebric and direct integration techniques. It is shown that projective collineations admitted by the above metric are the Killing vector fields.

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