Related papers: Stable fixed points of the Einstein flow with posi…
We complement a recent work on the stability of fixed points of the CMC-Einstein-$\Lambda$ flow. In particular, we modify the utilized gauge for the Einstein equations and remove a restriction on the fixed points whose stability we are able…
In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the Euler-Einstein system with a positive cosmological constant in 1 + 3 dimensions. The background…
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the 1 + 3 dimensional Euler-Einstein system with a positive cosmological constant. These background…
We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data…
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…
The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically…
In this paper we study cosmological solutions to the Einstein--Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly…
The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a…
We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear…
We review recent results relating linear stability to dynamical stability and the scalar curvature rigidity of Einstein manifolds. We discuss closed and open Einstein manifolds as well as complete noncompact Einstein manifolds which are…
We consider the vacuum Einstein flow with a positive cosmological constant on spatial manifolds of product form. In spatial dimension at least four we show the existence of continuous families of recollapsing models whenever at least one of…
Here we prove a global existence theorem for sufficiently small however fully nonlinear perturbations of a family of background solutions of the $`n+1$' vacuum Einstein equations in the presence of a positive cosmological constant…
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.…
We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $\Lambda<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static…
Recently, zero-point length cosmology has shown some positive insights into some non-singular aspects of the early Universe. In addition, topological defects are known to play a significant role by its presence as a part of the total energy…
Two recent articles \cite{ashtekar2015general, moncrief2019could} suggested an interesting dynamical mechanism within the framework of the vacuum Einstein flow (or Einstein-$\Lambda$ flow if a positive cosmological constant $\Lambda$ is…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…