Related papers: Singularities in cosmologies with interacting flui…
The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…
Analytic properties of physical quantities in the cosmic fluid such as energy density \rho(t) and Hubble parameter H(t) are investigated near the future singularity (Big Rip). Both 4D and 5D cosmologies are considered (the Randall-Sundrum…
We prove that for large enough data, the life span of smooth solutions to the Cauchy problem for the following two quasilinear hyperbolic systems is finite: (1) equations of relativistic compressible fluid dynamics, (2) equations of plasma…
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…
It has been known that a non-perfect fluid that accounts for dissipative viscous effects can evade a highly anisotropic chaotic mixmaster approach to a singularity. Viscosity is often simply parameterised in this context, so it remains…
The purpose of this study is to describe a perfect fluid matter distribution that leads to a constant curvature region, thanks to the effect of a non-minimal coupling. This distribution exhibits a density profile within the range found in…
We investigate the way big rips are approached in a fully inhomogeneous description of the space-time geometry. If the pressure and energy densities are connected by a (supernegative) barotropic index, the spatial gradients and the…
Parabolic geometric flows are smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of [CM6] and here is that, by bringing in the dynamical…
We study a cosmological model of gravity coupled to three, self-interacting scalar fields, one of them with negative kinetic term. The theory has cosmological solutions described by three-dimensional quadratic autonomous equations, leading…
A new cosmological solution of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I geometry and with perfect fluid as matter sources is presented. The matter is described by a…
We show that a class of 3+1 dimensional Friedmann-Robertson-Walker cosmologies can be embedded within a variety of solutions of string theory. In some realizations the apparent singularities associated with the big bang or big crunch are…
In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the…
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied (gr-qc/9903008, gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models with data at…
We prove that certain asymptotically flat initial data sets with nontrivial topology and/or differentiable structure collapse to form singularities. The class of such initial data sets is characterized by a new smooth invariant, the maximal…
Motivated by cosmological applications for interacting matters, an extension of the action functional for relativistic fluids is proposed to incorporate the physics of non-adiabatic processes and chemical reactions. The former are…
One or two negative mass singularities are found to occur in static inhomogeneous spatially closed solutions to the Einstein equations. The singularities produce a positive Komar mass, and this decreases the size of the cosmological…