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.

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.

Classification of non-conformally flat static plane symmetric perfect fluid solutions via proper conformal vector fields in f(T) gravity

2020 ◽  
Vol 17 (14) ◽  
pp. 2050218
Author(s):  
Murtaza Ali ◽  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
S. F. Hussain ◽  
Muhammad Ramzan
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Killing Vector ◽  
Flat Space ◽  
Conformally Flat ◽  
Field Equations ◽  
Plane Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Static Plane

The aim of this paper is to classify non-conformally flat static plane symmetric (SPS) perfect fluid solutions via proper conformal vector fields (CVFs) in [Formula: see text] gravity. For this purpose, first we explore some SPS perfect fluid solutions of the Einstein field equations (EFEs) in [Formula: see text] gravity. Second, we utilize these solutions to find proper CVFs. In this study, we found 16 cases. A detailed study of each case reveals that in three of these cases, the space-times admit proper CVFs whereas in the rest of the cases, either the space-times become conformally flat or they admit proper homothetic vector fields (HVFs) or Killing vector fields (KVFs). The dimension of CVFs for non-conformally flat space-times in [Formula: see text] gravity is four, five or six.

Classification of proper non-static cylindrically symmetric perfect fluid space-times via conformal vector fields in f(R) gravity

2020 ◽  
Vol 17 (10) ◽  
pp. 2050147 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
Shabeela Malik ◽  
Muhammad Ramzan ◽  
A. H. Kara
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Direct Integration ◽  
Cylindrically Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the [Formula: see text] gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the [Formula: see text] gravity.

A note on classification of teleparallel conformal symmetries in non-static plane symmetric space-times in the teleparallel theory of gravitation using diagonal tetrads

2016 ◽  
Vol 13 (04) ◽  
pp. 1650046 ◽  
Author(s):  
Ghulam Shabbir ◽  
Alamgeer Khan ◽  
M. Amer Qureshi ◽  
A. H. Kara
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Integration Technique ◽  
Plane Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravitation ◽  
Static Plane

In this paper, we explore teleparallel conformal vector fields in non-static plane symmetric space-times in the teleparallel theory of gravitation using the direct integration technique and diagonal tetrads. This study will also cover the static plane symmetric space-times as well. In the teleparallel theory curvature of the non-static plane symmetric space-times is zero and the presence of torsion allows more symmetries. In this study after solving the integrabilty conditions it turns out that the dimension of teleparallel conformal vector fields are 5, 6, 7 or 8.

A note on classification of spatially homogeneous rotating space-times in f(R) theory of gravity according to their proper conformal vector fields

2019 ◽  
Vol 16 (07) ◽  
pp. 1950111 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
Muhammad Ramzan ◽  
Ashfaque H. Bokhari
Keyword(s):  
Vector Fields ◽  
Space Time ◽  
Conformally Flat ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Spatially Homogeneous ◽  
Theory Of Gravity

In this paper, we present a study of proper conformal vector fields of spatially homogeneous rotating space-times in the [Formula: see text] theory of gravity. A total of six cases have been discussed in detail. It is found that the conformally non-flat spatially homogeneous rotating space-times do not admit proper conformal vector fields, while in a conformally flat case the space-time admits 15 independent conformal vector fields.

Conformal vector fields in proper non-static plane symmetric spacetimes in f(R) gravity

2020 ◽  
Vol 17 (05) ◽  
pp. 2050077 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
F. M. Mahomed ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Integration Approach ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity ◽  
Static Plane

Nonstatic plane symmetric spacetimes are considered to study conformal vector fields (VFs) in the [Formula: see text] theory of gravity. Firstly, we investigate some proper nonstatic plane symmetric spacetimes by solving the Einstein field equations (EFEs) in the [Formula: see text] theory of gravity using algebraic techniques. Secondly, we find CVFs of the obtained spacetimes by means of the direct integration approach. There exist seven cases. Studying each case in detail, we find that the CVFs are of dimension three, five, six and fifteen.

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.

Classification of vacuum classes of plane fronted gravitational waves via proper conformal vector fields in f(R) gravity

2019 ◽  
Vol 16 (10) ◽  
pp. 1950151 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
Muhammad Ramzan ◽  
Shabeela Malik
Keyword(s):  
Gravitational Waves ◽  
Vector Fields ◽  
Homothetic Vector ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Integration Techniques ◽  
Pp Wave ◽  
Wave Space ◽  
Theory Of Gravity

In this paper, we have studied proper conformal vector fields of pp-wave space-times in the [Formula: see text] theory of gravity using algebraic and direct integration techniques. From this study, we found that a very special class of pp-waves known as plane fronted gravitational waves (GWs) is a solution in the [Formula: see text] theory of gravity. In order to find proper conformal vector fields, plane GWs are further classified in ten cases. Studying each case in detail it turns out that in two cases proper conformal vector fields exist while in the rest of eight cases, conformal vector fields become homothetic 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.

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.

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