Bianchi Type I Magnetized Stiff Fluid Models with Bulk Viscosity in Lyra Geometry
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Bianchi Type I Magnetized Stiff Fluid Models with Bulk Viscosity in Lyra Geometry Raj Bali • Rajendra Vadhwani
Received: 10 January 2013 / Revised: 25 April 2013 / Accepted: 7 May 2013 / Published online: 15 October 2013 Ó The National Academy of Sciences, India 2013
Abstract In the present study, we have investigated Bianchi Type I cosmological model for stiff fluid or Zel’dovich fluid distribution with magnetic field and bulk viscosity in the frame work of Lyra geometry. To get the deterministic model, we have also assumed a condition that eigen value (r11 ) of shear tensor (rji ) is proportional to the expansion (h) in the model. This leads to A = (BC)n where A, B, C are metric potentials and n is a constant. The physical and geometrical aspects of the model in presence and absence of magnetic field and bulk viscosity are also discussed. Keywords Bianchi I Magnetized Stiff fluid Bulk viscosity Lyra geometry
Introduction Einstein derived his field equations of general relativity by geometrizing gravitation. Weyl [1] developed a theory to unify gravitation and electromagnetism in a single space– time geometry inspired by the idea of Einstein for geometrizing gravitation. But Weyl theory was not accepted due to non-integrability of length transfer. Lyra [2] introduced a gauge function i.e. a displacement vector in Riemannian space–time which removed the non-integrability condition of a vector under parallel transport. In this way, Riemannian geometry was modified by introducing a gauge function and this new geometry was named as Lyra geometry. Sen [3] developed a new scalar tensor theory of R. Bali (&) R. Vadhwani Department of Mathematics, University of Rajasthan, Jaipur 302004, India e-mail: [email protected]
gravitation and constructed a field equation in the frame work of Lyra geometry analogue to Einstein’s field equation of General Relativity. Halford [4] has pointed out that constant displacement vector /i in Lyra geometry plays the role of cosmological constant in General Relativity treatment. Cosmological models in the frame work of Lyra geometry, have been investigated by number of authors viz. Beesham [5], Singh and Singh [6], Rahman and Bera [7], Rahman et al. [8], Pradhan et al. [9, 10], Bali and Chandnani [11]. The distribution of matter and radiation could be treated as perfect fluid in the large scale. However, the observed physical phenomena such as the large entropy per baryon and the remarkable degree of isotropy of the cosmic microwave background radiation suggests the dissipative effects in cosmology. Also, there are several processes which give rise to viscous effects. These are decoupling of neutrinos during the radiation era, decoupling of radiation and matter during recombination era. Bulk viscosity is associated with the Grand Unified Field Theory (GUT) phase transition and string creation. The effect of bulk viscosity on the cosmological evolution has been studied by number of authors and we are quoting few here viz. Misner [12, 13], Padmanabhan and Chitre [14
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