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We construct spherically symmetric, static solutions to the Einstein-Vlasov system with non-vanishing cosmological constant $\Lambda$. The results are divided as follows. For small $\Lambda>0$ we show existence of globally regular solutions…
The dynamics of solutions of the Einstein-Vlasov system with Bianchi I symmetry is discussed in the case of massive or massless particles. It is shown that in the case of massive particles the solutions are asymptotic to isotropic dust…
A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in…
We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein…
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
Einstein-Vlasov system is solved for a homogeneous isotropic spacetime with positive curvature. In the case of the Universe consisting of massless particles the equation for R(t) is solved analytically.
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…
An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of…
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…
In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk…
In this paper, we study the past asymptotics of $(2+1)$-dimensional solutions to the Einstein scalar-field Vlasov system which are close to Friedman-Lema\^itre-Robertson-Walker spacetimes on an initial hypersurface diffeomorphic to a closed…
We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust…
Multi-parameter solutions to the Einstein equations in 2+1 dimensions are presented, with stress-energy given by a rotating dust with negative cosmological constant. The matter density is uniform in the corotating frame, and the ratio of…
In this paper, we study the evolution of asymptotically AdS initial data for the spherically symmetric Einstein--massless Vlasov system for $\Lambda<0$, with reflecting boundary conditions imposed on timelike infinity $\mathcal{I}$, in the…
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
We establish the future nonlinear stability of a large class of FLRW models as solutions to the Einstein-Dust system. We consider the case of a vanishing cosmological constant, which in particular implies that the expansion rate of the…
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…