Version 1
: Received: 7 January 2021 / Approved: 8 January 2021 / Online: 8 January 2021 (11:21:41 CET)
How to cite:
Sadhukhan, S.; Kar, A. Hamiltonian Formalism of Bianchi Type I Model for Fluid Bulk and Shearing Viscosity. Preprints2021, 2021010146. https://doi.org/10.20944/preprints202101.0146.v1
Sadhukhan, S.; Kar, A. Hamiltonian Formalism of Bianchi Type I Model for Fluid Bulk and Shearing Viscosity. Preprints 2021, 2021010146. https://doi.org/10.20944/preprints202101.0146.v1
Sadhukhan, S.; Kar, A. Hamiltonian Formalism of Bianchi Type I Model for Fluid Bulk and Shearing Viscosity. Preprints2021, 2021010146. https://doi.org/10.20944/preprints202101.0146.v1
APA Style
Sadhukhan, S., & Kar, A. (2021). Hamiltonian Formalism of Bianchi Type I Model for Fluid Bulk and Shearing Viscosity. Preprints. https://doi.org/10.20944/preprints202101.0146.v1
Chicago/Turabian Style
Sadhukhan, S. and Alokananda Kar. 2021 "Hamiltonian Formalism of Bianchi Type I Model for Fluid Bulk and Shearing Viscosity" Preprints. https://doi.org/10.20944/preprints202101.0146.v1
Abstract
In this paper we will consider the cosmic fluid to be dissipating i.e it has both bulk and shearing viscosity. We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for cosmic fluid which is dissipating i.e it has both shearing and bulk viscosity. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion of Bianchi type 1 in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. By this transformation we can express the mass to be moving in a scalar potential field. This definition helps us to explain the nature of expansion of universe during cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved. In the case of bulk and shearing viscous fluid we get the solution of damped harmonic oscillator after the cosmological inflation.Part I contains the calculations of bulk viscous fluids and Part II contains the calculations of bulk and shearing viscous fluid.At the end we have also provided the relation of shearing and expansion.Part III will give the approximation of low viscosity to solve the viscous fluid problem.
Keywords
General theory of relativity ; Bianchi type 1 ; Hamiltonian formalism ; bulk viscosity ; cosmology ; Fluid dynamics ; Isotropic and Anisotropic cosmology ; shearing viscosity
Subject
Physical Sciences, Astronomy and Astrophysics
Copyright:
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.
