arXiv subjects

Ikjyot Singh Kohli

Publications and source records attributed to Ikjyot Singh Kohli.

23 records · Page 2Linked to original sources

arXiv2014

On The Dynamics of a Closed Viscous Universe

We use a dynamical systems approach based on the method of orthonormal frames to study the dynamics of a non-tilted Bianchi Type IX cosmological model with a bulk and shear viscous fluid source. We begin by completing a detailed fix-point analysis which give the local sinks, sources and saddles of the dynamical system. We then analyze the global dynamics by finding the $α$-and $ω$-limit sets which give an idea of the past and future asymptotic behavior of the system. The fixed points were found to be a flat Friedmann-LeMaître-Robertson-Walker (FLRW) solution, Bianchi Type $II$ solution, Kasner circle, Jacobs disc, Bianchi Type $VII_{0}$ solutions, and several closed FLRW solutions in addition to the Einstein static universe solution. Each equilibrium point was described in both its expanding and contracting epochs. We conclude the paper with some numerical experiments that shed light on the global dynamics of the system along with its heteroclinic orbits. With respect to past asymptotic states, we were able to conclude that the Jacobs disc in the expanding epoch was a source of the system along with the flat FLRW solution in a contracting epoch. With respect to future asymptotic states, we were able to show that the flat FLRW solution in an expanding epoch along with the Jacobs disc in the contracting epoch were sinks of the system. We were also able to demonstrate a new result with respect to the Einstein static universe. Namely, we gave certain conditions on the parameter space such that the Einstein static universe has an associated stable subspace. We were however, not able to conclusively say anything about whether a closed FLRW model could be a past or future asymptotic state of the model.

gr-qc↗

arXiv2014

The Future Asymptotic Behaviour of a Non-Tilted Bianchi Type IV Viscous Model

The future asymptotic behaviour of a non-titled Bianchi Type IV viscous fluid model is analyzed. In particular, we consider the case of a viscous fluid without heat conduction, and constant expansion-normalized bulk and shear viscosity coefficients. We show using dynamical systems theory that the only future attracting equilibrium points are the flat Friedmann-LeMaitre (FL) solution, the open FL solution and the isotropic Milne universe solution. We also show the bifurcations exist with respect to an increasing expansion-normalized bulk viscosity coefficient. It is finally shown through an extensive numerical analysis, that the dynamical system isotropizes at late times.

gr-qc↗

arXiv2014

A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model

We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe FLRW solution, and interestingly, a new solution to the Einstein Field equations involving non-zero magnetic fields, and non-zero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.

gr-qc↗

arXiv2012

Quantum Wavefunction for a Schwarzschild Black Hole

A pseudo-Riemannian manifold contains an inherent Hamiltonian structure within the symplectic manifold in the cotangent bundle corresponding to the metric. Using this structure, it is possible to define a Hamiltonian, which can be quantized, and substituted into The Schrodinger Equation. The wave function, despite having a very complicated structure, has the very interesting property where it vanishes at the Schwarzschild $(r=0)$ singularity. This demonstrates an apparent violation of Quantum Mechanics, in which information is required to be conserved, and gives further evidence of a wave function vanishing at the singularity point. In addition, we give conditions for this wave function vanishing in terms of quantum numbers. NOTE: It has been graciously pointed out that the techniques of transforming the Hamiltonian to an equivalent metric tensor is only valid for a Riemannian manifold, not the pseudo-Riemannian manifold as required by General Relativistic theories. Although, the specific mathematics used is completely valid in this paper, the correct approach would be to use the ADM techniques for Quantum Gravity. Updated version to follow!

gr-qc↗

arXiv2012

A Bianchi Type IV Viscous Fluid Model of The Early Universe

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 \emph{Raychaudhuri Equation}, \emph{generalized Friedmann equation}, \emph{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 to the present-day universe. We finally conclude by discussing The Penrose-Hawking singularity theorem, and show that the viscous universe under consideration necessarily emerged from a past singularity point.

astro-ph.CO↗