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 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 proper teleparallel conformal symmetry of spherically symmetric static spacetimes using diagonal tetrads

2020 ◽  
Vol 35 (28) ◽  
pp. 2050232
Author(s):  
Muhammad Amer Qureshi ◽  
Ghulam Shabbir ◽  
K. S. Mahomed ◽  
Taha Aziz
Keyword(s):  
Vector Fields ◽  
Conformal Symmetry ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Conformal Vector Field ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Conformal Vector ◽  
Conformal Vector Fields

We study proper teleparallel conformal vector fields in spherically symmetric static spacetimes. The main objective of this paper is to present the classification for the above-mentioned spacetimes. The problem has been examined by two methods: direct integration technique and diagonal tetrads. We show that the spherically symmetric static spacetimes do not admit proper teleparallel conformal vector field, so are actually the teleparallel killing vector fields.

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 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.

Conformal vector fields of some vacuum classes of static spherically symmetric space-times in f(T,B) gravity

2020 ◽  
Vol 17 (10) ◽  
pp. 2050149 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
Shabeela Malik ◽  
Muhammad Ramzan
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Killing Vector Fields ◽  
Integration Approach ◽  
Conformal Vector ◽  
Conformal Vector Fields

The aim of this paper is to investigate the conformal vector fields (CVFs) for some vacuum classes of static spherically symmetric space-times in [Formula: see text] gravity. First, we have explored the space-times by solving the Einstein field equations in [Formula: see text] gravity. These solutions have been obtained by imposing various conditions on the space-time components and selecting separable form of the bivariate function [Formula: see text]. Second, we find the CVFs of the obtained space-times via direct integration approach. The overall study reveals that there exist 17 cases. From these 17 cases, the space-times in five cases admit proper CVFs whereas in rest of the 12 cases, CVFs become Killing vector fields (KVFs). We have also calculated the torsion scalar and boundary term for each of the obtained solutions.

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.

scholarly journals Concircular vector fields for Kantowski–Sachs and Bianchi type-III spacetimes

2018 ◽  
Vol 15 (08) ◽  
pp. 1850126 ◽  
Author(s):  
Suhail Khan ◽  
Amjad Mahmood ◽  
Ahmad T. Ali
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Conformal Killing ◽  
Conformal Killing Vector ◽  
Killing Vector Fields ◽  
Type Iii ◽  
Conformal Killing Vector Fields ◽  
Metric Functions

This paper intends to obtain concircular vector fields (CVFs) of Kantowski–Sachs and Bianch type-III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields (CKVFs) are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that Kantowski–Sachs and Bianchi type-III spacetimes admit four-, six-, or fifteen-dimensional concircular vector fields. It is established that for Einstein spaces, every conformal Killing vector field is a concircular vector field. Moreover, it is explored that every concircular vector field obtained here is also a conformal Ricci collineation.

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.

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