Related papers: Static vacuum Einstein metrics on bounded domains
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static vacuum metrics with prescribed Bartnik boundary data. We then…
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.
We investigate the Bartnik stationary extension conjecture, which arises from the definition of the spacetime Bartnik mass for a compact region in a general initial data set satisfying the dominant energy condition. This conjecture posits…
We prove that given any smooth metric $\gamma$ and smooth positive function $H$ on $S^{2}$, there is a constant $\lambda > 0$, depending on $(\gamma, H)$, and an asymptotically flat solution $(M, g, u)$ of the static vacuum Einstein…
This is a survey on the correspondence between asymptotically complex hyperbolic Einstein metrics and CR structures on the boundary at infinity, which is the complex version of that between Poincar\'e-Einstein metrics and conformal…
We prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely, we obtain quantitative criteria under which the physical spacetime can be extended…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
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…
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…
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…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…
We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.
The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general method for analyzing boundary value problems for integrable…
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 describe static, brane--like, solutions to vacuum Einstein's equations in D = n + m + 2 dimensional spacetime with m \ge 2 and n \ge 1. These solutions have positive ADM mass but no horizon. The curvature invariants are finite everywhere…
Trapped surfaces are studied as inner boundary for the Einstein vacuum constraint equations. The trapped surface condition can be written as a non linear boundary condition for these equations. Under appropriate assumptions, we prove…
We investigate some cylindrically symmetric nonstationary and nonstatic solutions of Einstein field equations. We first study some physical properties of a solution which can be considered as Kasner generalization of static Levi-Civita…
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…