scholarly journals Classification of static plane symmetric space–times according to their matter collineations

2004 ◽  
Vol 45 (4) ◽  
pp. 1518-1531 ◽  
Author(s):  
M. Sharif
Keyword(s):  
Symmetric Space ◽  
Plane Symmetric ◽  
Matter Collineations ◽  
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.

Homothetic matter collineations of static plane symmetric spacetimes

2019 ◽  
Vol 16 (12) ◽  
pp. 1950182
Author(s):  
Tahir Hussain ◽  
Khudija Shaheen ◽  
Faiza Saleem
Keyword(s):  
Energy Momentum Tensor ◽  
Complete Classification ◽  
Momentum Tensor ◽  
Dimensional Algebra ◽  
Plane Symmetric ◽  
Matter Collineations ◽  
Symmetric Spacetimes ◽  
Static Plane ◽  
Symmetric Spacetime

In this paper, we present a complete classification of static plane symmetric spacetimes via their homothetic symmetries of the energy–momentum tensor, known as homothetic matter collineations (HMCs). The HMC equations for these spacetimes are derived and then solved by considering the degeneracy and non-degeneracy of the energy–momentum tensor. In the former case, we have obtained 6, 11 and infinite number of HMCs, while in the latter case, the solution of HMC equations yields 6-, 7-, 8-, 10- and 11-dimensional algebra of HMCs. The obtained HMCs generate some differential constraints involving the components of the energy–momentum tensor. Some examples of static plane symmetric spacetime metrics satisfying these constraints are provided and the physical interpretations of these metrics are discussed.

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.

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.

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