Related papers: A global conformal extension theorem for perfect f…
Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic…
We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity,…
We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant $\Lambda$. The role of viscous fluid and $\Lambda$ term in the…
The Borde-Guth-Vilenkin (BGV) theorem states that any spacetime with net positive expansion must be geodesically incomplete. We derive a new version of the theorem using the fluid flow formalism of General Relativity. The theorem is purely…
We investigate the necessary conditions for the two spacetimes, which are solutions to the Einstein field equations with an anisotropic matter source, to be related to each other by means of a conformal transformation. As a result, we…
We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
We prove a global in time existence theorem, for the initial value problem for the Einstein-Boltzmann system, with arbitrarily large initial data, in the homogeneous case, in a Bianchi type I space-time
The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. It is…
We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity. We first discuss necessary and sufficient…
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of…
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…
The global regularity problem for the Boussinesq system is a well known open problem in mathematical fluid dynamics. As a follow up to our work \cite{EJSI}, we give examples of finite-energy and Lipschitz continuous velocity field and…
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those…
In this paper, dark energy models of the universe filled with wet dark fluid are constructed in the framework of LRS Bianchi type-II space-time in General Theory of Relativity. A new equation of state modeled on the equation of state…
Pick an arbitrary timelike geodesic in an arbitrary spacetime. We demonstrate that there is a particular limiting process, an "ultra-local limit", in which the immediate neighborhood of the timelike geodesic can be "blown up" to yield a…
We consider equations of the type: \[\partial_t \omega = \omega R(\omega),\] for general linear operators $R$ in any spatial dimension. We prove that such equations almost always exhibit finite-time singularities for smooth and localized…
It is investigated the behaviour of the ``constants'' $G,$ $c$ and $\Lambda $ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a $c-$variable into the curvature tensor. Two…
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$ in the presence of anisotropic matter. By finding an appropriate constant of the motion, and…
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are…
Self-consistent solutions to interacting spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions…