scholarly journals SYMMETRIES OF LOCALLY ROTATIONALLY SYMMETRIC MODELS

2005 ◽  
Vol 14 (10) ◽  
pp. 1675-1684 ◽  
Author(s):  
M. SHARIF
Keyword(s):  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Interesting Case ◽  
Degenerate Case ◽  
Infinite Dimensional ◽  
Constraint Equations ◽  
Matter Collineations ◽  
Locally Rotationally Symmetric ◽  
Rotationally Symmetric

Matter collineations of locally rotationally symmetric space–times are considered. These are investigated when the energy–momentum tensor is degenerate. We know that the degenerate case provides infinite dimensional matter collineations in most of the cases. However, an interesting case arises where we obtain proper matter collineations. We also solve the constraint equations for a particular case to obtain some cosmological models.

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.

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.

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.

Weyl static axially symmetric field equations in modified f(T) gravity

2017 ◽  
Vol 14 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Saeed Nayeh ◽  
Mehrdad Ghominejad
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Radial Component ◽  
Momentum Tensor ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Torsion Scalar

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of [Formula: see text] gravity, where [Formula: see text] is torsion scalar. We will see that, for [Formula: see text] related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component [Formula: see text]. The solutions of some functions [Formula: see text] in which [Formula: see text] is a function of [Formula: see text] are obtained.

Conformal Ricci collineations in LRS Bianchi type V spacetimes with perfect fluid matter

2017 ◽  
Vol 32 (24) ◽  
pp. 1750124 ◽  
Author(s):  
Fawad Khan ◽  
Tahir Hussain ◽  
Sumaira Saleem Akhtar
Keyword(s):  
Perfect Fluid ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Collineations ◽  
Rotationally Symmetric ◽  
Fluid Matter ◽  
Type V ◽  
Bianchi Type V

Considering the perfect fluid as a source of energy–momentum tensor, we have classified locally rotationally symmetric (LRS) Bianchi type V spacetimes according to their conformal Ricci collineations (CRCs). It is shown that the LRS Bianchi type V spacetimes with perfect fluid matter admit 9- or 15-dimensional Lie algebra of CRCs when the Ricci tensor is non-degenerate, while the group of CRCs is infinite for degenerate Ricci tensor.

scholarly journals Spinors in Cylindrically Symmetric Space–Time

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 152
Author(s):  
Bijan Saha
Keyword(s):  
Gravitational Field ◽  
Symmetric Space ◽  
Spinor Field ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Type I ◽  
Nonlinear Spinor ◽  
Cylindrically Symmetric

We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the EMT imposes three-way restrictions either on the space–time geometry or on the components of the spinor field or on both. It should be noted that the analogical situation occurs in cosmology when the nonlinear spinor field is exploited as a source of gravitational field given by the Bianchi type-I cosmological model.

NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIME AND GLOBAL MONOPOLE

1998 ◽  
Vol 13 (08) ◽  
pp. 1221-1228
Author(s):  
SUBENOY CHAKRABORTY ◽  
LALIT BISWAS
Keyword(s):  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Einstein Equations ◽  
Symmetric Model ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Spherically Symmetric Model

Under the assumption of functional separability of the metric coefficients, we have solved the Einstein equations for nonstatic spherically symmetric model. The energy–momentum tensor for the monopole configuration is taken in the form [Formula: see text]. Also the trajectories have been studied in different situations.

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