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

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ahmad T. Ali
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Lie Group ◽  
Magnetic Permeability ◽  
Bianchi Type ◽  
Group Analysis ◽  
Type I ◽  
Lie Group Analysis ◽  
Bianchi Type I ◽  
New Class

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 coordinatesxandt. We have assumed thatF12is only nonvanishing component of electromagnetic field tensorFij. The Maxwell equations show thatF12is the function ofxalone whereas the magnetic permeabilityμ¯is the function ofxandtboth. The physical behavior of the obtained model is discussed.

scholarly journals Interaction of Bianchi type-I anisotropic cloud string cosmological model universe with electromagnetic field

2020 ◽  
Vol 17 (09) ◽  
pp. 2050133
Author(s):  
Kangujam Priyokumar Singh ◽  
Mahbubur Rahman Mollah ◽  
Rajshekhar Roy Baruah ◽  
Meher Daimary
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Model ◽  
Bianchi Type ◽  
Physical Parameters ◽  
Type I ◽  
Field Equations ◽  
Rest Energy ◽  
Model Universe ◽  
Bianchi Type I ◽  
String Cosmological Model

Here, we have investigated the interaction of Bianchi type-I anisotropic cloud string cosmological model universe with electromagnetic field in the context of general relativity. In this paper, the energy-momentum tensor is assumed to be the sum of the rest energy density and string tension density with an electromagnetic field. To obtain exact solution of Einstein’s field equations, we take the average scale factor as an integrating function of time. Also, the dynamics and significance of various physical parameters of model are discussed.

Concircular vector fields on Lorentzian manifold of Bianchi type-I spacetimes

2018 ◽  
Vol 33 (12) ◽  
pp. 1850063
Author(s):  
Amjad Mahmood ◽  
Ahmad T. Ali ◽  
Suhail Khan
Keyword(s):  
Differential Equations ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Lorentzian Manifold ◽  
Conformal Killing ◽  
Type I ◽  
Bianchi Type I ◽  
Conformal Killing Vector Fields ◽  
Metric Functions

Our aim in this paper is to obtain concircular vector fields (CVFs) on the Lorentzian manifold of Bianchi type-I spacetimes. For this purpose, two different sets of coupled partial differential equations comprising ten equations each are obtained. The first ten equations, known as conformal Killing equations are solved completely and components of conformal Killing vector fields (CKVFs) are obtained in different possible cases. These CKVFs are then substituted into second set of ten differential equations to obtain CVFs. It comes out that Bianchi type-I spacetimes admit four-, five-, six-, seven- or 15-dimensional CVFs for particular choices of the metric functions. In many cases, the CKVFs of a particular metric are same as CVFs while there exists few cases where proper CKVFs are not CVFs.

scholarly journals A new class of LRS Bianchi type-I cosmological models in Lyra geometry

2004 ◽  
Vol 49 (3-4) ◽  
pp. 332-342 ◽  
Author(s):  
Anirudh Pradhan ◽  
Anil Kumar Vishwakarma
Keyword(s):  
Bianchi Type ◽  
Lyra Geometry ◽  
Cosmological Models ◽  
Type I ◽  
Bianchi Type I ◽  
New Class

Lie Group Analysis of Natural Convection Heat and Mass Transfer in an Inclined Surface

2006 ◽  
Vol 11 (2) ◽  
pp. 201-212 ◽  
Author(s):  
S. Sivasankaran ◽  
M. Bhuvaneswari ◽  
P. Kandaswamy ◽  
E. K. Ramasami
Keyword(s):  
Natural Convection ◽  
Differential Equations ◽  
Lie Group ◽  
Numerical Solutions ◽  
Group Analysis ◽  
Convection Heat Transfer ◽  
Solute Concentration ◽  
Heat Transfer Fluid ◽  
Lie Group Analysis ◽  
Convection Heat

Natural convection heat transfer fluid flow past an inclined semiinfinite surface in the presence of solute concentration is investigated by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations by the translation and scaling symmetries. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. It is found that the velocity increases and temperature and concentration of the fluid decrease with an increase in the thermal and solutal Grashof numbers. The velocity and concentration of the fluid decrease and temperature increases with increase in the Schmidt number.

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