Related papers: Quiescent Big Bang formation in $2+1$ dimensions
These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…
There are three categories of mathematical results concerning quiescent big bang singularities: the derivation of asymptotics in a symmetry class; the construction of spacetimes given initial data on the singularity; and the proof of big…
For the three-dimensional vacuum free boundary problem with physical singularity that the sound speed is $C^{ {1}/{2}}$-H$\ddot{\rm o}$lder continuous across the vacuum boundary of the compressible Euler equations with damping, without any…
We construct new classes of exact cosmological solutions to five dimensional Einstein-Maxwell-dilaton theory with two coupling constants for the dilaton-Maxwell term and dilaton-cosmological constant term. All the solutions are…
We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions…
The quasi-isotropic inhomogeneous solution of the Einstein equations near a cosmological singularity in the form of a series expansion in the synchronous system of reference, first found by Lifshitz and Khalatnikov in 1960, is generalized…
We investigate solutions of the $5$--dimensional rotating Einstein-Vlasov system with an $R \times SU(2) \times U(1)$ isometry group. In a five-dimensional spacetime, there are two independent planes of rotation, thus, considering $U(1)$…
We present new evidence in support of the Penrose's strong cosmic censorship conjecture in the class of Gowdy spacetimes with $T^3$ spatial topology. Solving Einstein's equations perturbatively to all orders we show that asymptotically…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though…
We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions…
This article is the first of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. The results of the present article concern the asymptotic behaviour of solutions to linear systems of…
We prove nonlinear Lyapunov stability of a family of `$n+1$'-dimensional cosmological models of general relativity locally isometric to the Friedman Lema\^itre Robertson Walker (FLRW) spacetimes including a positive cosmological constant.…
An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture---in its usual broad formulation---is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat…
Using both numerical and analytical tools we study various features of static, spherically symmetric solutions of the Einstein-Vlasov system. In particular, we investigate the possible shapes of their mass-energy density and find that they…
This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the…
In this paper we perform a systematic study of vacuum spatially flat ((3+D)+1)-dimensional Einstein-Gauss-Bonnet cosmological models. We consider models which topologically are the product of two flat isotropic subspaces with different…
In this paper, we study the thermodynamical and mathematical consistencies for a non-singular early-time viscous cosmological model known as soft-Big Bang, which was previously found in [N. Cruz, E. Gonz\'alez, and J. Jovel, Phys. Rev. D…
A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…
In this paper we study the large-time behavior of classical solutions to the two-species Vlasov-Maxwell-Boltzmann system in the whole space $\R^3$. The existence of global in time nearby Maxwellian solutions is known from [34] in 2006.…