Related papers: A global conformal extension theorem for perfect f…
In this paper, we use our results concerning temporal foliations of causal sets in order to provide a new proof of Geroch's Theorem on temporal foliations in a globally hyperbolic spacetime.
We study solutions of the Friedmann equations in case of the homogeneous isotropic Universe filled with a perfect fluid. The main points concern the monotony properties of the solutions, the possibility to extend the solutions on all times…
Non-singular Bianchi type I solutions are found from the effective action with a superstring-motivated Gauss-Bonnet term. These anisotropic non-singular solutions evolve from the asymptotic Minkowski region, subsequently super-inflate, and…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
We consider the dynamics of a causal bulk viscous cosmological fluid filled constantly decelerating Bianchi type I space-time. The matter component of the Universe is assumed to satisfy a linear barotropic equation of state and the state…
In this paper we study the isotropisation of a Generalized Scalar-Tensor theory with a massive scalar field. We find it depends on a condition on the Brans-Dicke coupling function and the potential and show that asymptotically the metric…
This paper is a continuation of the works in \cite{Euler} and \cite{NS}, where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively.…
We study the classical and quantum cosmology of a universe in which the matter content is a perfect fluid and the background geometry is described by a Bianchi type I metric. To write the Hamiltonian of the perfect fluid we use the Schutz…
We consider the dynamics of a Bianchi type I spacetime in the presence of dilaton and magnetic fields. The general solution of the Einstein-Maxwell dilaton field equations can be obtained in an exact parametric form. Depending on the…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
The present status of the shear-free perfect fluid conjecture in general relativity is discussed: I give a review of recent work and present a new formalism which may provide a better understanding of the problems encountered.
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called…
We show that for any perfect fluid in a static spacetime, if the Einstein constraint equation is satisfied and the temperature of the fluid obeys Tolman's law, then the other components of Einstein's equation are implied by the assumption…
We look for necessary isotropisation conditions of Bianchi class $A$ models with curvature in presence of a massive and minimally coupled scalar field when a function $\ell$ of the scalar field tends to a constant, diverges monotonically or…
We study the well-posedness and the spatial behavior at infinity of perfect fluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spaces that allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. In…
The standard cosmological model is challenged by an ever-growing collection of observations, which invites (and stimulates) inquiry into possible additions and/or alterations. One such alteration comes from letting cosmic isotropy -- as…
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,…