Conformal vector fields of static spherically symmetric space-times in f(R, G) gravity

2020 ◽  
Vol 17 (08) ◽  
pp. 2050120
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
M. Ramzan ◽  
S. F. Hussain ◽  
Sabiha Qazi
Keyword(s):  
Symmetric Space ◽  
Current Literature ◽  
Vector Fields ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Symmetric Metrics

Assuming the most general form of static spherically symmetric space-times, we search for the conformal vector fields in [Formula: see text] gravity by means of algebraic and direct integration approaches. In this study, there exist six cases which on account of further study yield conformal vector fields of dimension four, six and fifteen. During this study, we also recovered some well-known static spherically symmetric metrics announced in the current literature.

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.

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.

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.

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.

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.

Existence of conformal vector fields of Bianchi type I space-times in f(R) gravity

2020 ◽  
Vol 17 (08) ◽  
pp. 2050113 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
S. Jamal ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Flat Space ◽  
Type I ◽  
Direct Integration ◽  
Conformally Flat ◽  
Bianchi Type I ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Integration Techniques

In this paper, Bianchi type I space-times in the [Formula: see text] theory of gravity are classified via conformal vector fields using algebraic and direct integration techniques. In this classification, we show that the conformal vector fields are of dimension four, five, six or fifteen. Additionally, we found that non-conformally flat Bianchi type I space-times admit conformal vector fields of dimension four, five or six. In the case of conformally flat or flat space-times, the dimension of the conformal vector fields is fifteen.

Conformal vector fields of static spherically symmetric perfect fluid space-times in modified teleparallel theory of gravity

2020 ◽  
Vol 17 (13) ◽  
pp. 2050202 ◽  
Author(s):  
Shabeela Malik ◽  
Fiaz Hussain ◽  
Ghulam Shabbir
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Gravity Models ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravity

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

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