60 70 63 v 1 1 7 Ju l 2 00 6 The General Solution of Bianchi Type III Vacuum Cosmology

- qc / 0 20 70 56 v 1 1 5 Ju l 2 00 2 The Mixmaster Universe in Five Dimensions Paul

We consider a five dimensional vacuum cosmology with Bianchi type-IX spatial geometry and an extra non-compact coordinate. Finding a new class of solutions, we examine and rule out the possibility of deterministic chaos. We interpret this result within the context of induced matter theory.

The General Solution of Bianchi Type V IIh Vacuum Cosmology

The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einsteins Field Equations (EFEs). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time repa...

ar X iv : g r - qc / 0 60 70 44 v 1 1 1 Ju l 2 00 6 Instabilities in numerical loop quantum cosmology

In this article we perform von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are i...

Automorphism Inducing Diffeomorphisms and the general solution of Bianchi Type III Vacuum Cosmology

A general method for solving the Cosmological Einstein’s Field Equations (EFE) in vacuum is presented, and is applied to the Bianchi Type III vacuum cosmology. As a result, the entire space of solutions for this model is found. This space is composed of two distinct, disconnected ,three-parameter families. Both of them admit four Killing vector Fields and no homothetic vector. One family repres...

0 40 70 95 v 1 2 6 Ju l 2 00 4 Lectures on Mathematical Cosmology