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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 918927, 8 pages
http://dx.doi.org/10.1155/2014/918927
Research Article

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

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt

Received 28 December 2013; Accepted 3 June 2014; Published 19 June 2014

Academic Editor: Maria Bruzón

Copyright © 2014 Ahmad T. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 and . We have assumed that is only nonvanishing component of electromagnetic field tensor . The Maxwell equations show that is the function of alone whereas the magnetic permeability is the function of and both. The physical behavior of the obtained model is discussed.