Related papers: Dynamics of a lattice Universe
We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and…
A new method of solving the Einstein-Friedmann dynamical equations of a spatially homogeneous and isotropic universe is presented. The method is applicable when the equation of state of the material content assumes the form P=(g -1) rho, g…
We present an analytical approximation formula for the growth function in a spatially flat cosmology with dust and a cosmological constant. Our approximate formula is written simply in terms of a rational function. We also show the…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
A physicaly reasonable interpretation is provided for the perfect fluid, sphericaly symmetric, conformally flat ``Stephani Universes''. The free parameters of this class of exact solutions are determined so that the ideal gas relation $p=n…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
We study the evolution of linear density fluctuations of free-streaming massive neutrinos at redshift of z<1000, with an explicit justification on the use of a fluid approximation. We solve the collisionless Boltzmann equation in an…
We establish a new model, which takes into account a dynamic (inertial) self-interaction of gravitating systems. The model is formulated by introduction of a new function depending on the square of the covariant derivative of the velocity…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We present the particular case of the Stephani solution for shear-free perfect fluid with uniform energy density and non-uniform pressure. Such models appeared as possible alternative to the consideration of the exotic forms of matter like…
We present a novel homogeneous and geometrically flat exact solution of Einstein's General Relativity equations for an ideal fluid. The solution, which describes an expanding/contracting hypercylinder, fits well with the observational…
In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for…
We propose a solution to the puzzle of dimensional reduction in the random field Ising model, inverting the question and asking: to what random problem in $D=d+2$ dimensions does a pure system in $d$ dimensions correspond? We consider two…
We study the effect of the slab topology $T\times R\times R$ of the Universe on the form of gravitational potentials and forces created by point-like masses. We obtain two alternative forms of solutions: one is based on the Fourier series…
A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics…
Observational cosmology provides us with a large number of high precision data which are used to derive models trying to reproduce ``on the mean'' our observable patch of the Universe. Most of these attempts are achieved in the framework of…
We consider scalar tensor theories of gravity assuming that the scalar field is non minimally coupled with gravity. We use this theory to study evolution of a flat homogeneous and isotropic universe. In this case the dynamical equations can…
In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…