The classification of static plane symmetric space–times according to their Ricci collineations

1995 ◽  
Vol 36 (10) ◽  
pp. 5812-5828 ◽  
Author(s):  
Taha Bin Farid ◽  
Asghar Qadir ◽  
M. Ziad
Keyword(s):  
Symmetric Space ◽  
Ricci Collineations ◽  
Plane Symmetric ◽  
Static Plane

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 study of energy conditions in static plane symmetric space–times via homothetic symmetries

2019 ◽  
Vol 34 (35) ◽  
pp. 1950238
Author(s):  
Tahir Hussain ◽  
Uzma Nasib ◽  
Muhammad Farhan ◽  
Ashfaque H. Bokhari
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Field Equations ◽  
New Approach ◽  
Plane Symmetric ◽  
Homothetic Vector ◽  
Integration Techniques ◽  
Static Plane

The aim of this study is twofold. First, we use a new approach to study the homothetic vector fields (HVFs) of static plane symmetric space–times by an algorithm which we have developed using the Maple platform. The interesting feature of this algorithm is that it provides the most general form of metrics admitting HVFs as compared to those obtained in an earlier study where direct integration techniques were used. Second, the obtained metrics are used in Einstein’s field equations to compute the energy–momentum tensor and it is shown how the parameters involved in the obtained space–time metrics are associated with certain important energy conditions.

Homothetic Ricci collineations in non-static plane symmetric spacetimes with perfect fluid matter

2018 ◽  
Vol 15 (05) ◽  
pp. 1850075
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar
Keyword(s):  
Perfect Fluid ◽  
Ricci Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Collineations ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Fluid Matter ◽  
Static Plane ◽  
Degenerate Cases

In this paper, we investigate homothetic Ricci collineations (HRCs) for non-static plane symmetric spacetimes. The source of the energy–momentum tensor is assumed to be a perfect fluid. Both degenerate as well as non-degenerate cases are considered and the HRC equations are solved in different cases. It is concluded that these spacetimes may possess 6, 7, 8, 10 or 11 HRCs in non-degenerate case, while they admit seven or infinite number of HRCs for degenerate Ricci tensor.

scholarly journals Geometrical/Physical Interpretation of the Conserved Quantities Corresponding to Noether Symmetries of Plane Symmetric Space-Times

2017 ◽  
Vol 2017 ◽  
pp. 1-40 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze ◽  
Andrés Vargas
Keyword(s):  
Symmetric Space ◽  
Lie Algebras ◽  
Physical Interpretation ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Riemann Curvature ◽  
Plane Symmetric ◽  
Structure Constants ◽  
Curvature Tensors

The aim of this paper is to give the geometrical/physical interpretation of the conserved quantities corresponding to each Noether symmetry of the geodetic Lagrangian of plane symmetric space-times. For this purpose, we present a complete list of plane symmetric nonstatic space-times along with the generators of all Noether symmetries of the geodetic Lagrangian. Additionally, the structure constants of the associated Lie algebras, the Riemann curvature tensors, and the energy-momentum tensors are obtained for each case. It is worth mentioning that the list contains all classes of solutions that have been obtained earlier during the classification of plane symmetric space-times by isometries and homotheties.

Proper conformal Killing vectors in static plane symmetric space–times

2017 ◽  
Vol 191 (1) ◽  
pp. 620-629 ◽  
Author(s):  
T. Hussain ◽  
S. Khan ◽  
A. H. Bokhari ◽  
G. A. Khan
Keyword(s):  
Symmetric Space ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Plane Symmetric ◽  
Conformal Killing Vectors ◽  
Static Plane

Classification of static plane symmetric spacetime via Noether gauge symmetries

2016 ◽  
Vol 13 (09) ◽  
pp. 1650111 ◽  
Author(s):  
Adil Jhangeer ◽  
Nazish Iftikhar ◽  
Tayyaba Naz
Keyword(s):  
Radial Functions ◽  
Plane Symmetric ◽  
Linear Partial Differential Equations ◽  
Gauge Symmetries ◽  
First Case ◽  
Gauge Term ◽  
Static Plane ◽  
Noether Operators ◽  
Symmetric Spacetime

In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions [Formula: see text], [Formula: see text] and [Formula: see text]. Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between [Formula: see text], [Formula: see text] and [Formula: see text]. For all cases, different forms of unknown functions of radial factor [Formula: see text] are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1–4 is presented.

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.

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