Related papers: Spatially Homogeneous Dynamics: A Unified Picture
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
All classes of spatially homogeneous space-time models are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of complete separation of variables according to type (2.1).…
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of…
We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotropic matter model that naturally generalizes perfect fluids.…
We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in…
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to…
The necessary and sufficient conditions for a perfect fluid solution to define a spatially-homogeneous cosmology are achieved. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling of these…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
We present a dynamical analysis in terms of new expansion-normalized variables for homogeneous and anisotropic Bianchi-I spacetimes in $f(R)$ gravity in the presence of anisotropic matter. With a suitable choice of the evolution parameter,…
We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein's…
We investigate some new similarity inhomogeneous solutions of anisotropic dark energy and perfect fluid in Bianchi type-I space-time. Three different equation of state parameters along the spatial directions are introduced to quantify the…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states…
We briefly show how we can obtain Hamiltonians for spatially compact locally homogeneous vacuum spacetimes. The dynamical variables are categorized into the curvature parameters and the Teichm\"{u}ller parameters. While the Teichm\"{u}ller…