Killing vector fields and the Einstein-Maxwell field equations with perfect fluid source

1976 ◽  
Vol 7 (4) ◽  
pp. 345-359 ◽  
Author(s):  
J. Wainwright ◽  
P. E. A. Yaremovicz
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Killing Vector ◽  
Maxwell Field ◽  
Field Equations ◽  
Killing Vector Fields ◽  
Fluid Source

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.

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.

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 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.

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.

scholarly journals Curvature tensor for the spacetime of general relativity

2017 ◽  
Vol 14 (05) ◽  
pp. 1750078 ◽  
Author(s):  
Zafar Ahsan ◽  
Musavvir Ali
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Vector Fields ◽  
Killing Vector ◽  
Conformal Killing ◽  
Field Equations ◽  
Text Structures ◽  
Conformal Killing Vector Fields ◽  
Perfect Fluid Spacetime

In the differential geometry of certain [Formula: see text]-structures, the role of [Formula: see text]-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing [Formula: see text]-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing [Formula: see text]-tensor have also been considered. The divergence of [Formula: see text]-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved [Formula: see text]-tensor represents either an Einstein space or a Friedmann-Robertson-Walker cosmological model.

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