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Ahmad T. Ali

Publications and source records attributed to Ahmad T. Ali.

15 recordsLinked to original sources
arXiv2020

Plane symmetric cosmological models

In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the similarity reductions and obtain exact solutions in connection to the evolutionary scenario of the universe. The special feature of the study is that it deals with the electromagnetic energy of the inhomogeneous universe through the non-vanishing component of electromagnetic field tensor $F_{12}$ and assumes that the free gravitational field is of Petrov type-II non-degenerate. We have found that the electromagnetic field tensor is positive and increasing function of time. To validate the solution set, we examine with detailed discussions several physical as well as geometrical features of a specific sub-case of the model.

physics.gen-ph↗
arXiv2017

Invariant Bianchi type I models in $f\left(R,T\right)$ Gravity

In this paper, we search the existence of invariant solutions of Bianchi type I space-time in the context of $f\left(R,T\right)$ gravity. The exact solution of the Einstein's field equations are derived by using Lie point symmetry analysis method that yield two models of invariant universe for symmetries $X^{(1)}$ and $X^{(3)}$. The model with symmetries $X^{(1)}$ begins with big bang singularity while the model with symmetries $X^{(3)}$ does not favour the big bang singularity. Under this specification, we find out at set of singular and non singular solution of Bianchi type I model which present several other physically valid features within the framework of $f\left(R,T\right)$.

physics.gen-ph↗
arXiv2015

Some Invariant String Cosmological Models in Cylindrically Symmetric Space-time

In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and eometrical properties of the models derived in the paper. The solutions, at least one of them, are interesting physically as they can explain the accelerating as well as singularity free Universe.

gr-qc↗
arXiv2013

Symmetry Group Analysis for perfect fluid Inhomogeneous Cosmological Models in General Relativity

In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. The isovector fields of Einstein's field equation for the models under consideration are derived. A new class of exact solutions of Einstein's field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.

gr-qc↗
arXiv2009

Similar Curves With Variable Transformations

In this paper, we define a new family of curves and call it a {\it family of similar curves with variable transformation} or briefly {\it SA-curves}. Also we introduce some characterizations of this family and we give some theorems. This definition introduces a new classification of a space curve. Also, we use this definition to deduce the position vectors of plane curves, general helices and slant helices, as examples of a similar curves with variable transformation.

math.DG↗
arXiv2009

Determination of time-like helices from intrinsic equations in Minkowski 3-Space

In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space E$^3_1$ satisfies a vector differential equation of fourth order. The general solution of mentioned vector differential equation has not yet been found. By special cases, we determine the parametric representation of the general helices from the intrinsic equations (i.e. curvature and torsion are functions of arc-length) of the time-like curve. Moreover, we give some examples to illustrate how to find the position vector from the intrinsic equations of general helices.

math.DG↗
arXiv2009

Some Characterizations of Rectifying Spacelike Curves in the Minkowski Space-Time

In this paper, we define a rectifying spacelike curve in the Minkowski space-time $E_1^4$ as a curve whose position vector always lies in orthogonal complement $N^{\bot}$ of its principal normal vector field $N$. In particular, we study the rectifying spacelike curves in $E_1^4$ and characterize such curves in terms of their curvature functions.

math.DG↗
arXiv2009

Determination of the position vectors of general helices from intrinsic equations in $\e^3$

In this paper, we prove that the position vector of every space curve satisfies a vector differential equation of fourth order. Also, we determine the parametric representation of the position vector $ψ=\Big(ψ_1,ψ_2,ψ_3\Big)$ of general helices from the intrinsic equations $κ=κ(s)$ and $τ=τ(s)$ where $κ$ and $τ$ are the curvature and torsion of the space curve $ψ$, respectively. Our result extends some knwown results. Moreover, we give four examples to illustrate how to find the position vector from the intrinsic equations of general helices.

math.DG↗
arXiv2009

Slant helices in Euclidean 4-space $E^4$

We consider a unit speed curve $α$ in Euclidean four-dimensional space $E^4$ and denote the Frenet frame by $\{T,N,B_1,B_2\}$. We say that $α$ is a slant helix if its principal normal vector $N$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures.

math.DG↗
arXiv2009

Some Characterizations of Cylindrical Helices in $E^n$

We consider a unit speed curve $α$ in Euclidean $n$-dimensional space $E^n$ and denote the Frenet frame by $\{v_1,...,v_n\}$. We say that $α$ is a cylindrical helix if its tangent vector $v_1$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures.

math.DG↗
arXiv2008

Timelike $B_2$-slant helices in Minkowski space $E_1^4$

We consider a unit speed timelike curve $α$ in Minkowski 4-space $E_1^4$ and denote the Frenet frame of $α$ by $\{T,N,B_1,B_2\}$. We say that $α$ is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction $U$ of $E_1^4$. In this work we study those helices where the function $ $ is constant and we give different characterizations of such curves.

math.DG↗
arXiv2008

On slant helices in Minkowski space $E_1^3$

We consider a curve $α=α(s)$ in Minkowski 3-space $E_1^3$ and denote by $\{T,N,B}$ the Frenet frame of $α$. We say that $α$ is a slant helix if there exists a fixed direction $U$ of $E_1^3$ such that the function $ $ is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $α$.

math.DG↗