Friday, July 27, 2012

1207.6132 (Ikjyot Singh Kohli et al.)

A Qualitative Analysis of The Bianchi Type IV Viscous Fluid Model    [PDF]

Ikjyot Singh Kohli, Michael C. Haslam
We are interested in formulating a viscous model of the universe based on The Bianchi Type IV algebra. We first begin by considering a congruence of fluid lines in spacetime, upon which, analyzing their propagation behaviour, we derive the famous Raychaudhuri equation, but, in the context of viscous fluids. We will then go through in great detail the topological and algebraic structure of a Bianchi Type IV algebra, by which we will derive the corresponding structure and constraint equations. From this, we will look at The Einstein field equations in the context of orthonormal frames, and derive the resulting dynamical equations: The Raychaudhuri Equation, generalized Friedmann equation, shear propagation equations, and a set of non-trivial constraint equations. We show that for cases in which the bulk viscous pressure is significantly larger than the shear viscosity, this cosmological model isotropizes asymptotically.
View original: http://arxiv.org/abs/1207.6132

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