arXiv subjects

Mudhahir Al-Ajmi

Publications and source records attributed to Mudhahir Al-Ajmi.

8 recordsLinked to original sources

arXiv2024

Exploring Self-Gravitating Cylindrical Structures in Modified Gravity: Insights from Scalar-Vector-Tensor Theory

We investigate static cylindrical solutions within an extended theory of modified gravity. By incorporating various coupling functions through a straightforward boost symmetry approach, we establish the equations of motion in a self-consistent manner and subsequently determine the linear scalar field profile. Utilizing analytical methods, we solve the system of equations for the metric functions and the $U(1)$ gauge field, revealing their dependence on Bessel's functions. To comprehend gravito-objects exhibiting cylindrical symmetry, we develop a perturbative framework aimed at identifying all nontrivial solutions for the scalar profiles. Introducing first-order truncated perturbation equations for the gauge field, synchronized with metric gauges and electromagnetic field considerations, we demonstrate their integrability and obtain solutions through quadrature. Our findings suggest the feasibility of obtaining self-gravitating cylindrical structures within the scalar-vector-tensor theory.

gr-qc↗

arXiv2018

The quaternionic commutator bracket and its implications

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, \emph{viz.} $\widetildeψ=(\frac{i}{c}\,ψ_0\,,\vecψ)$, represents a state of a particle with orbital angular momentum, $L=3\,\hbar$, resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector $\vecψ$, points along the direction of $\vec{L}$. When a charged particle is placed in an electromagnetic fields the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov-Bohm and Aharonov-Casher effects.

physics.gen-ph↗

arXiv2018

The modified electromagnetism and the emergent longitudinal wave

The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca, Vlaenderen & Waser and Arbab theories are investigated.

physics.gen-ph↗

arXiv2012

Quaterionic Construction of the W(F_4) Polytopes with Their Dual Polytopes and Branching under the Subgroups B(B_4) and W(B_3)*W(A_1)

4-dimensional $F_{4} $ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary \textbf{$W(F_{4})$} orbit under the Coxeter groups $W(B_{4} $ and $W(B_{3}) \times W(A_{1})$ have been presented. The role of group theoretical technique and the use of quaternions have been emphasized

math-ph↗

arXiv2011

Branching of the W(H4) Polytopes and Their Dual Polytopes under the Coxeter Groups W(A4) and W(H3) Represented by Quaternions

4-dimensional H4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(H4) where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary W(H4) orbit into three dimensions is made preserving the icosahedral subgroup W(H3) and the tetrahedral subgroup W(A3), the latter follows a branching under the Coxeter group W(A4) . The dual polytopes of the semi-regular and quasi-regular H4 polytopes have been constructed.

math-ph↗

arXiv2011

4D-Polytopes and Their Dual Polytopes of the Coxeter Group $W(A_{4})$ Represented by Quaternions

4-dimensional $A_{4}$ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(A_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Projection of an arbitrary $W(A_{4})$ orbit into three dimensions is made using the subgroup $W(A_{3})$. A generalization of the Catalan solids for 3D polyhedra has been developed and dual polytopes of the uniform $A_{4}$ polytopes have been constructed.

math-ph↗

arXiv2009

Quaternionic Representation of Snub 24-Cell and its Dual Polytope Derived From E_8 Root System

Vertices of the 4-dimensional semi-regular polytope, \textit{snub 24-cell} and its symmetry group $W(D_{4}):C_{3} $ of order 576 are represented in terms of quaternions with unit norm. It follows from the icosian representation of \textbf{$E_{8} $} root system. The quaternionic root system of $H_{4} $ splits as the vertices of 24-cell and the \textit{snub 24-cell} under the symmetry group of the \textit{snub 24-cell} which is one of the maximal subgroups of the group \textbf{$W(H_{4})$} as well as $W(F_{4})$. It is noted that the group is isomorphic to the\textbf{}semi-direct product of the Weyl group of $D_{4}$ with the cyclic group of order 3 denoted by $W(D_{4}):C_{3} $, the Coxeter notation for which is $[3,4,3^{+}]$. We analyze the vertex structure of the \textit{snub 24-cell} and decompose the orbits of \textbf{$W(H_{4})$} under the orbits of $W(D_{4}):C_{3} $. The cell structure of the snub 24-cell has been explicitly analyzed with quaternions by using the subgroups of the group $W(D_{4}):C_{3} $. In particular, it has been shown that the dual polytopes 600-cell with 120 vertices and 120-cell with 600 vertices decompose as 120=24+96 and 600=24+96+192+288 respectively under the group $W(D_{4}):C_{3} $. The dual polytope of the \textit{snub 24-cell} is explicitly constructed. Decompositions of the Archimedean $W(H_{4})$ polytopes under the symmetry of the group $W(D_{4}):C_{3} $ are given in the appendix.

math-ph↗

arXiv2009

Grand Antiprism and Quaternions

Vertices of the 4-dimensional semi-regular polytope, the \textit{grand antiprism} and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the \textbf{$E_{8} $} root system which decomposes into two copies of the root system of $H_{4} $. The symmetry of the \textit{grand antiprism} is a maximal subgroup of the Coxeter group $W(H_{4})$. It is the group $Aut(H_{2} \oplus H'_{2})$ which is constructed in terms of 20 quaternionic roots of the Coxeter diagram $H_{2} \oplus H'_{2}$. The root system of $H_{4} $ represented by the binary icosahedral group \textit{I}of order 120, constitutes the regular 4D polytope 600-cell. When its 20 quaternionic vertices corresponding to the roots of the diagram $H_{2} \oplus H'_{2}$ are removed from the vertices of the 600-cell the remaining 100 quaternions constitute the vertices of the\textit{grand antiprism}. We give a detailed analysis of the construction of the cells of the\textit{grand antiprism} in terms of quaternions. The dual polytope of the \textit{grand antiprism} has been also constructed.

math-ph↗