Bianchi type VI 0 cosmological model with electromagnetic field and variable deceleration parameter in general theory of
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ORIGINAL PAPER
Bianchi type VI0 cosmological model with electromagnetic field and variable deceleration parameter in general theory of relativity E A Hegazy1*
and F Rahaman2
1
Mathematics Department, Faculty of Science, Minia University, El-Minia 61519, Egypt
2
Department of Mathematics, Jadavpur University, Kolkata, West Bengal 700032, India Received: 30 April 2019 / Accepted: 09 August 2019
Abstract: Bianchi type VI0 cosmological model in the presence of the electromagnetic field in the theory of relativity is studied. For the current flow along z-axis, F12 is the only nonvanishing component of Fij (the magnetic field). An exact solution of the field equations is given by considering the deceleration parameter as a linear function of t in the form q ¼ 1 þ m kt where m and k are constants. The entropy S and the thermodynamic functions (enthalpy, Gibbs energy and Helmholtz energy) of the universe are calculated and studied. Also, physical and geometrical properties of our models are studied. Keywords: General theory of relativity; Einstein field equations; Bianchi type VI0 cosmological models; Variable deceleration parameter; Entropy; Electromagnetic field PACS Nos.: 04.20.-q; 04.20.Jb; 03.50.De; 05.70.Ce
1. Introduction In 1916, Einstein [1] introduced the general theory of relativity which succeeded in geometrizing gravitation by identifying the metric tensor with gravitational potentials. Since that time, several authors have dealt with space-times in the relativity theory with different forms for the energy momentum tensor which represents the distribution of the matter content. Why time-dependent deceleration parameter is expected? In the past, the expansion of universe was decelerating in nature and in the present time it is accelerating and as a result the deceleration parameter q must show signature flipping which is consistent with CMB anisotropies and type Ia supernovae (SNe Ia) observations [2–4]. Some authors studied cosmological models in the theory of relativity and modified theories of relativity with timedependent deceleration parameter (q). In the case when the relation between the deceleration parameter (q) and the Hubble parameter (H) was considered in a linear form, in
*Corresponding author, E-mail: [email protected]; [email protected]
the f(R, T) theory of gravity, LRS Bianchi type I model was studied by Tiwari et al. [5], Bianchi type I model in the presence of a dissipative fluid with time-dependent cosmological ‘‘constant’’ K in the relativity theory was given by Tiwari et al. [6] and exact solutions of the field equations in the relativity theory for homogeneous and anisotropic Bianchi type I model were studied by Tiwari et al. [7]. Pradhan et al. [8] studied the transit behavior of the universe. They have studied the universe which is modeled by Bianchi type I cosmological models and considered the pffiffiffiffiffiffiffi 2n scale factor as aðtÞ ¼ tn et which yields q ¼ 1 þ ðkþtÞ 2. In the presence of viscous fluid, Bianchi type I space-times with variable deceleration parameter
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