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.

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.

Homothetic Ricci collineations of non-static spherically symmetric spacetimes with perfect fluid matter

2018 ◽  
Vol 33 (34) ◽  
pp. 1850196
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Fawad Khan
Keyword(s):  
Perfect Fluid ◽  
Infinite Number ◽  
Ricci Tensor ◽  
Spherically Symmetric ◽  
Ricci Collineations ◽  
Symmetric Spacetimes ◽  
Fluid Matter ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

Non-static spherically symmetric spacetimes with perfect fluid matter are considered and their homothetic Ricci collineations (HRCs) are investigated for degenerate as well as non-degenerate Ricci tensor. The present analysis shows that, for non-degenerate Ricci tensor, the possible number of HRCs admitted by these spacetimes is 5, 6 or 7, while they possess 4, 11 or otherwise infinite number of HRCs when the Ricci tensor is degenerate.

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.

scholarly journals Quasilocal conservation laws in cosmology: A first look

2020 ◽  
Vol 29 (14) ◽  
pp. 2043029
Author(s):  
Marius Oltean ◽  
Hossein Bazrafshan Moghaddam ◽  
Richard J. Epp
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Conservation Laws ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Fluid Matter ◽  
Stress Energy Momentum Tensor

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

scholarly journals Non-static spherically symmetric spacetimes and their conformal Ricci collineations

2019 ◽  
Vol 9 (2) ◽  
pp. 393-400 ◽  
Author(s):  
Fawad Khan ◽  
Tahir Hussain ◽  
Ashfaque Hussain Bokhari ◽  
Sumaira Saleem Akhtar
Keyword(s):  
Vector Field ◽  
Infinite Number ◽  
Ricci Tensor ◽  
Spherically Symmetric ◽  
Ricci Collineations ◽  
Symmetric Spacetimes ◽  
Integrability Conditions ◽  
Fluid Matter ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

Abstract For a perfect fluid matter, we present a study of conformal Ricci collineations (CRCs) of non-static spherically symmetric spacetimes. For non-degenerate Ricci tenor, a vector field generating CRCs is found subject to certain integrability conditions. These conditions are then solved in various cases by imposing certain restrictions on the Ricci tensor components. It is found that non-static spherically symmetric spacetimes admit 5, 6 or 15 CRCs. In the degenerate case, it is concluded that such spacetimes always admit infinite number of CRCs.

scholarly journals Spacetimes Admitting Concircular Curvaure Tensor in f(R) Gravity

2022 ◽  
Vol 9 ◽  
Author(s):  
Uday Chand De ◽  
Sameh Shenawy ◽  
H. M. Abu-Donia ◽  
Nasser Bin Turki ◽  
Suliman Alsaeed ◽  
...  
Keyword(s):  
Energy Density ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Ricci Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Isotropic Pressure ◽  
Concircular Curvature Tensor ◽  
Fluid Spacetimes

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

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.

Charged gravastars in f(R,T,RμνTμν) gravity

2021 ◽  
pp. 2150084
Author(s):  
Z. Yousaf ◽  
M. Z. Bhatti
Keyword(s):  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Equations Of State ◽  
Mathematical Formulation ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
De Sitter ◽  
The Stability ◽  
Physical Features ◽  
Modified Theory

We explore the aspects of the electromagnetism on the stability of gravastar in a particular modified theory, i.e. [Formula: see text] where [Formula: see text], [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. We assume a spherically symmetric static metric coupled comprising of perfect fluid in the presence of electric charge. The purpose of this paper is to extend the results of [S. Ghosh, F. Rahaman, B. K. Guha and S. Ray, Phys. Lett. B 767 (2017) 380.] to highlight the effects of [Formula: see text] gravity in the formation of charged gravastars. We demonstrated the mathematical formulation, utilizing different equations of state, for the three respective regions (i.e. inner, shell, exterior) of the gravastar. We have matched smoothly the interior de Sitter and the exterior Reissner–Nordström metric at the hypersurface. At the end we extracted few conclusions by working on the physical features of the charged gravastar, mathematically and graphically.

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