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.

scholarly journals PROPER MATTER COLLINEATIONS OF PLANE SYMMETRIC SPACETIMES

2007 ◽  
Vol 22 (24) ◽  
pp. 1813-1819
Author(s):  
M. SHARIF ◽  
TARIQ ISMAEEL
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Plane Symmetric ◽  
Matter Collineations ◽  
Symmetric Spacetimes ◽  
Finite Dimensional

We investigate matter collineations of plane symmetric spacetimes when the energy–momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in these cases are either four, six or ten in which four are isometries and the rest are proper.

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.

Homothetic matter collineations of LRS Bianchi type I spacetimes

2017 ◽  
Vol 32 (37) ◽  
pp. 1750197 ◽  
Author(s):  
Tahir Hussain ◽  
Waqas Rahim
Keyword(s):  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Complete Classification ◽  
Momentum Tensor ◽  
Type I ◽  
Bianchi Type I ◽  
Matter Collineations ◽  
Rotationally Symmetric ◽  
Integrability Conditions

A complete classification of locally rotationally symmetric (LRS) Bianchi type I spacetimes via homothetic matter collineations (HMCs) is presented. For non-degenerate energy–momentum tensor, a general form of the vector field generating HMCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 6-, 7-, 8-, 10- or 11-dimensional Lie algebra of HMCs. When the energy–momentum tensor is degenerate, two cases give 6 and 11 HMCs, while the remaining cases produce infinite number of HMCs. Some LRS Bianchi type I metrics are provided admitting HMCs.

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.

Homothetic matter collineations of LRS Bianchi type V spacetimes with perfect fluid source

2019 ◽  
Vol 34 (38) ◽  
pp. 1950312
Author(s):  
Tahir Hussain ◽  
Shehzad Ahmad ◽  
Fawad Khan
Keyword(s):  
Perfect Fluid ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Dimensional Algebra ◽  
Fluid Source ◽  
Matter Collineations ◽  
Rotationally Symmetric ◽  
Type V ◽  
Bianchi Type V

For a perfect fluid source, we have investigated the homothetic matter collineations (HMCs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes. For degenerate energy–momentum tensor, two cases arise. In one case, the solution of HMC equations yields 11-dimensional algebra of HMCs while in the second case, we have infinite number of HMCs. When the energy–momentum tensor is non-degenerate, we have four cases, each giving five-dimensional algebra of HMCs. Some LRS Bianchi type V metrics are provided admitting HMCs.

scholarly journals SPHERICALLY SYMMETRIC GRAVITATIONAL COLLAPSE

2009 ◽  
Vol 24 (19) ◽  
pp. 1533-1542 ◽  
Author(s):  
M. SHARIF ◽  
KHADIJA IQBAL
Keyword(s):  
Surface Energy ◽  
Gravitational Collapse ◽  
Curvature Tensor ◽  
Energy Momentum Tensor ◽  
Extrinsic Curvature ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
Tangential Pressure ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with g00 = 1. Israel's junction conditions are used to develop this formalism. The formulas for extrinsic curvature tensor are obtained. The general form of the surface energy–momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained show the regions for the collapse and expansion of the shell.

Classification of Variational Conservation Laws of General Plane Symmetric Spacetimes

2017 ◽  
Vol 68 (3) ◽  
pp. 335 ◽  
Author(s):  
Usamah S. Al-Ali ◽  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
Ghulam Shabbir
Keyword(s):  
Conservation Laws ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
General Plane

scholarly journals Approximate Noether symmetries from geodetic Lagrangian for plane symmetric spacetimes

2015 ◽  
Vol 12 (10) ◽  
pp. 1550124 ◽  
Author(s):  
Farhad Ali ◽  
Tooba Feroze
Keyword(s):  
Conformal Factor ◽  
Noether Symmetries ◽  
Plane Symmetric ◽  
First Order ◽  
Symmetric Spacetimes ◽  
General Plane ◽  
Symmetric Spacetime ◽  
Conformal Plane ◽  
General Time

Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time-conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed,5–6 where they obtained approximate Noether symmetries from Lagrangian for a particular plane symmetric static spacetime. In the present paper, the most general plane symmetric static spacetime is considered and perturbed it by introducing a general time-conformal factor eϵf(t), where ϵ is very small which causes the perturbation in the spacetime. Taking the perturbation up to the first-order, we find all Lagrangian for plane symmetric spacetimes for which approximate Noether symmetries exist.

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