scholarly journals Classification of static cylindrically symmetric spacetimes in f(R) theory of gravity by conformal motions with perfect fluid matter

2018 ◽  
Vol 8 (2) ◽  
pp. 115-123 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
Muhammad Ramzan
Keyword(s):  
Perfect Fluid ◽  
Cylindrically Symmetric ◽  
Symmetric Spacetimes ◽  
Fluid Matter ◽  
Theory Of Gravity ◽  
Cylindrically Symmetric Spacetimes

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

Classification of proper non-static cylindrically symmetric perfect fluid space-times via conformal vector fields in f(R) gravity

2020 ◽  
Vol 17 (10) ◽  
pp. 2050147 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
Shabeela Malik ◽  
Muhammad Ramzan ◽  
A. H. Kara
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Direct Integration ◽  
Cylindrically Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields

In this paper, we classify proper non-static cylindrically symmetric (CS) perfect fluid space-times via conformal vector fields (CVFs) in the [Formula: see text] gravity. In order to classify the space-times, we use the algebraic and direct integration approaches. In the process of classification, there exist 23 cases for which the considered space-times become proper non-static. By studying each case in detail, we find that the conformal vector fields are of dimensions two, three and fifteen in the [Formula: see text] gravity.

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 DIRAC ANALYSIS AND INTEGRABILITY OF GEODESIC EQUATIONS FOR CYLINDRICALLY SYMMETRIC SPACETIMES

2003 ◽  
Vol 12 (08) ◽  
pp. 1431-1444 ◽  
Author(s):  
UGUR CAMCI
Keyword(s):  
Symplectic Structure ◽  
Equations Of Motion ◽  
First Order ◽  
Geodesic Equations ◽  
Cylindrically Symmetric ◽  
Symmetric Spacetimes ◽  
Constraint Analysis ◽  
Stationary Spacetime ◽  
Cylindrically Symmetric Spacetimes ◽  
Geodesic Equations Of Motion

Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of motion are integrated, and found some solutions for Lewis, Levi-Civita, and Van Stockum spacetimes.

Conformal cylindrically symmetric spacetimes in modified gravity

2015 ◽  
Vol 30 (37) ◽  
pp. 1550202 ◽  
Author(s):  
Murat Metehan Türkog̃lu ◽  
Melis Ulu Dog̃ru
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Casimir Force ◽  
Conformal Symmetry ◽  
Vacuum State ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Symmetric Spacetimes ◽  
Cylindrically Symmetric Spacetime ◽  
Symmetric Spacetime

We investigate cylindrically symmetric spacetimes in the context of [Formula: see text] gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle–Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special [Formula: see text] function convenient to [Formula: see text]-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different [Formula: see text] models. Finally, geometrical and physical results of the solutions are discussed.

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