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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/918927 |
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| 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 |