Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry

We find a new class of invariant inhomogeneous Bianchi type-I cosmological models in electromagnetic field with variable magnetic permeability. For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Ein...

Full description

Saved in:
Bibliographic Details
Main Author: Ahmad T. Ali
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/918927
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832549597010984960
author Ahmad T. Ali
author_facet Ahmad T. Ali
author_sort Ahmad T. Ali
collection DOAJ
description We find a new class of invariant inhomogeneous Bianchi type-I cosmological models in electromagnetic field with variable magnetic permeability. For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Einstein field equations) invariant. With the help of canonical variables associated with these generators, the assigned system of PDEs is reduced to ordinary differential equations (ODEs) whose simple solutions provide nontrivial solutions of the original system. A new class of exact (invariant-similarity) solutions have been obtained by considering the potentials of metric and displacement field as functions of coordinates x and t. We have assumed that F12 is only nonvanishing component of electromagnetic field tensor Fij. The Maxwell equations show that F12 is the function of x alone whereas the magnetic permeability μ¯ is the function of x and t both. The physical behavior of the obtained model is discussed.
format Article
id doaj-art-91c4d9c8ef8e44369e16053306fc144c
institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-91c4d9c8ef8e44369e16053306fc144c2025-02-03T06:10:59ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/918927918927Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra GeometryAhmad T. Ali0Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe find a new class of invariant inhomogeneous Bianchi type-I cosmological models in electromagnetic field with variable magnetic permeability. For this, Lie group analysis method is used to identify the generators that leave the given system of nonlinear partial differential equations (NLPDEs) (Einstein field equations) invariant. With the help of canonical variables associated with these generators, the assigned system of PDEs is reduced to ordinary differential equations (ODEs) whose simple solutions provide nontrivial solutions of the original system. A new class of exact (invariant-similarity) solutions have been obtained by considering the potentials of metric and displacement field as functions of coordinates x and t. We have assumed that F12 is only nonvanishing component of electromagnetic field tensor Fij. The Maxwell equations show that F12 is the function of x alone whereas the magnetic permeability μ¯ is the function of x and t both. The physical behavior of the obtained model is discussed.http://dx.doi.org/10.1155/2014/918927
spellingShingle Ahmad T. Ali
Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry
Abstract and Applied Analysis
title Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry
title_full Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry
title_fullStr Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry
title_full_unstemmed Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry
title_short Invariant Inhomogeneous Bianchi Type-I Cosmological Models with Electromagnetic Fields Using Lie Group Analysis in Lyra Geometry
title_sort invariant inhomogeneous bianchi type i cosmological models with electromagnetic fields using lie group analysis in lyra geometry
url http://dx.doi.org/10.1155/2014/918927
work_keys_str_mv AT ahmadtali invariantinhomogeneousbianchitypeicosmologicalmodelswithelectromagneticfieldsusingliegroupanalysisinlyrageometry