PROPER PROJECTIVE SYMMETRY IN SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

2005 ◽  
Vol 14 (08) ◽  
pp. 1451-1463 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Special Class ◽  
Vector Fields ◽  
Space Time ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Integration Techniques ◽  
Projective Vector ◽  
Static Space

A study of proper projective symmetry in spherically symmetric static space–times is given by using algebraic and direct integration techniques. It is shown that a special class of the above space–time admits proper projective vector fields.

Proper projective symmetry in the most general non-static spherically symmetric four-dimensional Lorentzian manifolds

2016 ◽  
Vol 13 (02) ◽  
pp. 1650009 ◽  
Author(s):  
Ghulam Shabbir ◽  
F. M. Mahomed ◽  
M. A. Qureshi
Keyword(s):  
Symmetric Space ◽  
Special Class ◽  
Space Time ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Lorentzian Manifolds

A study of proper projective symmetry in the most general form of non-static spherically symmetric space-time is given using direct integration and algebraic techniques. In this study, we show that when the above space-time admits proper projective symmetry it becomes a very special class of static spherically symmetric space-times.

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.

Conformal vector fields of static spherically symmetric space-times in f(R, G) gravity

2020 ◽  
Vol 17 (08) ◽  
pp. 2050120
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
M. Ramzan ◽  
S. F. Hussain ◽  
Sabiha Qazi
Keyword(s):  
Symmetric Space ◽  
Current Literature ◽  
Vector Fields ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Symmetric Metrics

Assuming the most general form of static spherically symmetric space-times, we search for the conformal vector fields in [Formula: see text] gravity by means of algebraic and direct integration approaches. In this study, there exist six cases which on account of further study yield conformal vector fields of dimension four, six and fifteen. During this study, we also recovered some well-known static spherically symmetric metrics announced in the current literature.

PROPER PROJECTIVE SYMMETRY IN THE SCHWARZSCHILD METRIC

2006 ◽  
Vol 21 (23) ◽  
pp. 1795-1802 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Direct Integration ◽  
Killing Vector Fields ◽  
Schwarzschild Metric ◽  
Integration Techniques ◽  
Projective Collineations

A study of proper projective symmetry in the Schwarzschild metric is given by using algebric and direct integration techniques. It is shown that projective collineations admitted by the above metric are the Killing vector fields.

THE GENERALIZED SPHERICALLY-SYMMETRIC METRIC

2020 ◽  
Vol 22 (4) ◽  
pp. 223-226
Author(s):  
M.M. Khashaev
Keyword(s):  
Lie Algebra ◽  
Spherical Symmetry ◽  
Vector Fields ◽  
Killing Vector ◽  
Space Time ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Parameter Group ◽  
Killing Vectors ◽  
Spherically Symmetric Metric

Four parameter group of transformations containing rotations and time translations is consi[1]dered due to spherical symmetry and stationarity of the space-time metric. It is found that there exists such a quartet of Killing vector fields which constitute the Lie algebra of the transforma[1]tion group and in which space-like vectors are not orthogonal to the time-like one. The metric corresponding to the Lie algebra of Killing vectors is composed. It is shown that the metric is non-static.

Proper projective symmetry in LRS Bianchi type V spacetimes

2018 ◽  
Vol 33 (13) ◽  
pp. 1850073 ◽  
Author(s):  
Ghulam Shabbir ◽  
K. S. Mahomed ◽  
F. M. Mahomed ◽  
R. J. Moitsheki
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Riemann Tensor ◽  
Direct Integration ◽  
Killing Vector Fields ◽  
Rotationally Symmetric ◽  
Projective Vector ◽  
Type V ◽  
Bianchi Type V

In this paper, we investigate proper projective vector fields of locally rotationally symmetric (LRS) Bianchi type V spacetimes using direct integration and algebraic techniques. Despite the non-degeneracy in the Riemann tensor eigenvalues, we classify proper Bianchi type V spacetimes and show that the above spacetimes do not admit proper projective vector fields. Here, in all the cases projective vector fields are Killing vector fields.

Existence of conformal vector fields of Bianchi type I space-times in f(R) gravity

2020 ◽  
Vol 17 (08) ◽  
pp. 2050113 ◽  
Author(s):  
Ghulam Shabbir ◽  
Fiaz Hussain ◽  
S. Jamal ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Flat Space ◽  
Type I ◽  
Direct Integration ◽  
Conformally Flat ◽  
Bianchi Type I ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Integration Techniques

In this paper, Bianchi type I space-times in the [Formula: see text] theory of gravity are classified via conformal vector fields using algebraic and direct integration techniques. In this classification, we show that the conformal vector fields are of dimension four, five, six or fifteen. Additionally, we found that non-conformally flat Bianchi type I space-times admit conformal vector fields of dimension four, five or six. In the case of conformally flat or flat space-times, the dimension of the conformal vector fields is fifteen.

scholarly journals Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

Sign in / Sign up

Export Citation Format

Share Document