Related papers: Local existence and uniqueness for exterior static…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
The global existence of smooth solutions to the vacuum free boundary problem with physical singularity of compressible Euler equations with damping and gravity is proved in space dimensions $n=1, 2, 3$, for the initial data being small…
In this article, we are interested in the Einstein vacuum equations on a Lorentzian manifold displaying $\mathbb{U}(1)$ symmetry. We identify some freely prescribable initial data, solve the constraint equations and prove the existence of a…
We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system…
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a…
We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is bounded and initially constant near the…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsvath-Schucking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new…
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…
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 investigate the local regularity of pointed spacetimes, that is, time-oriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein…
We study series of the stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent with the exterior solutions in some class of the scalar-tensor theories of…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
We discuss simple vacuum solutions to the Einstein Equations in five dimensional space-times compactified in two different ways. In such spaces, one black hole phase and more then one black string phase may exist. Several old metrics are…
This article is dedicated to solving the Einstein constraint equations with apparent horizon boundaries and freely specified mean curvature. The main novelty is that we study the conformal constraint equations assuming only low regularity.
The assumption that a solution to the Einstein equations is static (or stationary) very strongly constrains the asymptotic behaviour of the metric. It is shown that one need only impose very weak differentiability and decay conditions {\it…
We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the…