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Ghulam Shabbir

Publications and source records attributed to Ghulam Shabbir.

At least 19 recordsLinked to original sources
arXiv2019

A note on some perfect fluid Kantowski-Sachs and Bianchi type III space-times and their conformal vector fields in f(R) theory of gravity

The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski-Sachs and Bianchi type III space-times in the f(R) theory of gravity using direct integration technique. In this study there exists only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of six cases conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.

gr-qc↗
arXiv2017

A note on proper affine symmetry in Bianchi types VIII and IX space-times

We consider the most general form of Bianchi types VIII and IX space-times for studying proper affine symmetry by using holonomy and decomposability, the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper affine symmetry in the above space-times it is shown that there exists only one possibilty when the above space-times admit proper affine vector field.

gr-qc↗
arXiv2015

Proper curvature collineations in non-static plane symmetric space-times

The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each non static case of the above space-times it is shown that when the above space-times admit proper curvature collineations, they form an infinite dimensional vector space.

math-ph↗
arXiv2015

A note on proper curvature collineations in Bianchi type IV space-times

Curvature collineations of Bianchi type IV space-times are investigated using the rank of the 6X6 Riemann matrix and direct integration technique. From the above study it follows that the Bianchi type IV space-times possesses only one case when it admits proper curvature collineations. It is shown that proper curvature collineations form an infinite dimensional vector space.

gr-qc↗
arXiv2015

Conservation of Hamiltonian using Continuous Galerkin Petrov time discretization scheme

Continuous Galerkin Petrov time discretization scheme is tested on some Hamiltonian systems including simple harmonic oscillator, Kepler's problem with different eccentricities and molecular dynamics problem. In particular, we implement the fourth order Continuous Galerkin Petrov time discretization scheme and analyze numerically, the efficiency and conservation of Hamiltonian. A numerical comparison with some symplectic methods including Gauss implicit Runge-Kutta method and general linear method of same order is given for these systems. It is shown that the above mentioned scheme, not only preserves Hamiltonian but also uses the least CPU time compared with upto-date and optimized methods.

math.NA↗
arXiv2013

Proper curvature symmetry in non-static cylindrically symmetric Lorentzian manifolds

We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature symmetry in each case of the above space-times it is shown that when the above space-times admit proper curvature symmetry, they form an infinite dimensional vector space.

gr-qc↗
arXiv2013

Classification of non conformally flat cylindrically symmetric non static space-times according to their proper conformal motions

In this paper we considered the most general form of non conformally flat cylindrically symmetric non-static space-times to study proper conformal motions using direct integration technique. We have shown that very special classes for cylindrically symmetric space-times admit proper conformal motions. This classification also covers non-static and static plane symmetric space-times. In [9] it was claimed that non conformally flat plane symmetric static space-times do not admit proper conformal motion. Here it is also shown that static and non static plane symmetric space-times admit proper conformal motions. We also discuss the Lie algebra in each case.

gr-qc↗
arXiv2008

Proper projective collineation in non-static spherically symmetric space-times

We investigate the proper projective collineation in non-static spherically symmetric space-times using direct integration and algebraic techniques. Studying projective collineation in the above space-times, it is shown that the space-times which admit proper projective collineations turn out to be very special classes of static spherically symmetric space-times.

gr-qc↗
arXiv2007

Weyl Projective Curvature Symmetry in FRW k=0 Model

A study of proper Weyl projective curvature collineations in FRW k=0 space-time is given using the rank of Weyl projective curvature matrix and direct integration techniques. It is shown that a very special class of the above space-time admits proper Weyl projective curvature collineation.

gr-qc↗
arXiv2006

Proper Conformal Vector fields in Bianchi Type I Space-Times

Direct integration technique is used to study the proper conformal vector fields in non conformally flat Bianchi type-1 space-times. Using the above mentioned technique we have shown that a very special class of the above space-time admits proper conformal vector fields.

gr-qc↗
arXiv2006

Proper Weyl Collineations in Kantowski-Sachs and Bianchi Type III Space-Times

A study of proper Weyl collineations in Kantowski-Sachs and Bianchi type III space-times is given by using the rank of the 6X6 Weyl matrix and direct integration techniques. Studying proper Weyl collineations in each of the above space-times, it is shown that there exists no such possibility when the above space-times admit proper Weyl collineations.

gr-qc↗