Related papers: On the Bartnik extension problem for the static va…
We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…
We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial…
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…
Consider a triple of "Bartnik data" $(\Sigma, \gamma,H)$, where $\Sigma$ is a topological 2-sphere with Riemannian metric $\gamma$ and positive function $H$. We view Bartnik data as a boundary condition for the problem of finding a compact…
By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations…
We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical…
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 prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
In this paper we continue earlier investigations of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by R\'{a}cz. Motivated by the strong evidence from these works that the resulting vacuum initial…
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…
A number of recent observations have suggested that the Einstein's theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to…
We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorship, non-linear stability, new constructions of solutions of…
The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm large classes of boundary hypersurfaces are static regular. In…