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 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.

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 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.

scholarly journals MATTER INHERITANCE SYMMETRIES OF SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

2006 ◽  
Vol 21 (12) ◽  
pp. 2645-2657 ◽  
Author(s):  
M. SHARIF
Keyword(s):  
Energy Momentum Tensor ◽  
Complete Classification ◽  
Momentum Tensor ◽  
Conformal Killing ◽  
Spherically Symmetric ◽  
Metric Tensor ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Conformal Killing Vectors ◽  
Static Space

In this paper we discuss matter inheritance collineations by giving a complete classification of spherically symmetric static space–times by their matter inheritance symmetries. It is shown that when the energy–momentum tensor is degenerate, most of the cases yield infinite dimensional matter inheriting symmetries. It is worth mentioning here that two cases provide finite dimensional matter inheriting vectors even for the degenerate case. The nondegenerate case provides finite dimensional matter inheriting symmetries. We obtain different constraints on the energy–momentum tensor in each case. It is interesting to note that if the inheriting factor vanishes, matter inheriting collineations reduce to be matter collineations already available in the literature. This idea of matter inheritance collineations turn out to be the same as homotheties and conformal Killing vectors are for the metric tensor.

Anisotropic magnetized sources in general relativity: An exact description for the magnetized vacuum

2019 ◽  
Vol 28 (07) ◽  
pp. 1950090 ◽  
Author(s):  
D. Alvear Terrero ◽  
P. Bargueño ◽  
E. Contreras ◽  
A. Pérez Martínez ◽  
G. Quintero Angulo
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Symmetric Case ◽  
Plane Symmetric ◽  
Exact Description

In this work, we have constructed exact geometries which describe magnetized matter within General Relativity, specifically in an almost-plane-symmetric case. Although the use of this geometry imposes some constraints on the components of the energy–momentum tensor, it allows to describe some physically interesting situations in which the magnetized vacuum is relevant.

scholarly journals LIE SYMMETRIES OF THE ENERGY–MOMENTUM TENSOR FOR PLANE SYMMETRIC STATIC SPACETIMES

2005 ◽  
Vol 14 (05) ◽  
pp. 797-816 ◽  
Author(s):  
K. SAIFULLAH
Keyword(s):  
Lie Algebra ◽  
Explicit Form ◽  
Vector Fields ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The Other ◽  
Ricci Collineations ◽  
Plane Symmetric ◽  
Curvature Collineations ◽  
Paper Plane

Matter collineations (MCs) are the vector fields along which the energy–momentum tensor remains invariant under Lie transport. Invariance of the metric, the Ricci and the Riemann tensors have been studied extensively and the vectors along which these tensors remain invariant are called Killing vectors (KVs), Ricci collineations (RCs) and curvature collineations (CCs), respectively. In this paper, plane symmetric static spacetimes have been studied for their MCs. Explicit form of MCs together with the Lie algebra admitted by them has been presented. Examples of spacetimes have been constructed for which MCs have been compared with their RCs and KVs. The comparison shows that neither of the sets of RCs and MCs contains the other, in general.

MATTER COLLINEATIONS OF BIANCHI V SPACETIME

2005 ◽  
Vol 14 (06) ◽  
pp. 1023-1036 ◽  
Author(s):  
UGUR CAMCI
Keyword(s):  
Finite Number ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Degenerate Case ◽  
Killing Vectors ◽  
Matter Collineations ◽  
Bianchi V

Matter collineations of the Bianchi V spacetime are studied according to degenerate or non-degenerate energy–momentum tensor. We have found that in degenerate case there are infinitely many matter collineations, whereas two cases give finite number of matter collineations which are five and six. When the energy–momentum tensor is non-degenerate, we obtain either four, five, six or seven independent matter collineations, out of which three are minimal Killing vectors and the rest are proper matter collineations.

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.

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.

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