Proper Curvature Collineations of Plane Symmetric Static Spacetime in F(R) Theory of Gravity

2018 ◽  
Vol 50 (001) ◽  
pp. 73-78
Author(s):  
M. RAMZAN ◽  
A. NAZIR ◽  
M. R. MUFTI
Keyword(s):  
Plane Symmetric ◽  
Curvature Collineations ◽  
Theory Of Gravity ◽  
Proper Curvature

scholarly journals PROPER CURVATURE COLLINEATIONS IN NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIMES

2008 ◽  
Vol 23 (05) ◽  
pp. 749-759 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. RAMZAN
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Infinite Dimensional ◽  
Riemann Matrix ◽  
Integration Techniques ◽  
Curvature Collineations ◽  
Proper Curvature

A study of nonstatic spherically symmetric space–times according to their proper curvature collineations is given by using the rank of the 6×6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each case of the above space–times it is shown that when the above space–times admit proper curvature collineations, they turn out to be static spherically symmetric and form an infinite dimensional vector space. In the nonstatic cases curvature collineations are just Killing vector fields.

scholarly journals PROPER CURVATURE COLLINEATIONS IN KANTOWSKI–SACHS AND BIANCHI TYPE III SPACETIMES

2007 ◽  
Vol 22 (11) ◽  
pp. 807-817 ◽  
Author(s):  
GHULAM SHABBIR ◽  
ABU BAKAR MEHMOOD
Keyword(s):  
Bianchi Type ◽  
Dimensional Vector ◽  
Direct Integration ◽  
Dimensional Vector Space ◽  
Infinite Dimensional ◽  
Type Iii ◽  
Riemann Matrix ◽  
Integration Techniques ◽  
Curvature Collineations ◽  
Proper Curvature

A study of Kantowski–Sachs and Bianchi type III spacetimes according to their proper curvature collineations is given by using the rank of the 6×6 Riemann matrix and direct integration techniques. It is shown that when the above spacetimes admit proper curvature collineations, they form an infinite dimensional vector space.

Classification of curvature collineations of plane symmetric static spacetimes

2000 ◽  
Vol 41 (4) ◽  
pp. 2167-2172 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Abdul R. Kashif ◽  
Asghar Qadir
Keyword(s):  
Plane Symmetric ◽  
Curvature Collineations

A note on proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in f(R, T) theory of gravity

2019 ◽  
Vol 34 (24) ◽  
pp. 1950189 ◽  
Author(s):  
M. Jamil Khan ◽  
Ghulam Shabbir ◽  
M. Ramzan
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Killing Vector ◽  
The Other ◽  
Direct Integration ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Homothetic Vector ◽  
Theory Of Gravity

The purpose of this paper is to find proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in the [Formula: see text] theory of gravity by using direct integration technique. In this study, there exist six cases. Studying each case in detail, we found that in four cases proper homothetic vector fields exist while in the other two cases homothetic vector fields become Killing vector fields.

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.

Dust static plane symmetric solutions and their conformal vector fields in f(R) theory of gravity

2018 ◽  
Vol 33 (37) ◽  
pp. 1850222 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
F. M. Mahomed ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Conformally Flat ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity ◽  
Static Plane

We first find the dust solutions of static plane symmetric spacetimes in the theory of f(R) gravity. Then using the direct integration technique on the solutions obtained, we deduce the conformal vector fields. This is performed in the context of f(R) theory of gravity. There exist six cases. Out of these, in five cases the spacetimes become conformally flat and admit 15 conformal vector fields, whereas in the sixth case, conformal vector fields become Killing vector fields.

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