Related papers: On the Bartnik extension problem for the static va…
The spherically symmetric perturbations in the spatially flat Friedman models are considered. It is assumed that the Friedmannian density and pressure are related through a linear equation of state. The perturbation is joined smoothly with…
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,…
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the…
We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have…
This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first.…
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action…
Big Bang models of the Universe predict rapid domination by curvature, a paradox known as the flatness problem. Solutions to this problem usually leave the Universe exactly flat for every practical purpose. Explaining a nearly but not…
The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions…
Local solutions are a vivid and long-living topic in gravitational physics. We consider exact static pseudo-spherically symmetric solutions of semi-classical Einstein's equations in presence of the trace anomaly contribution. We investigate…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
By assuming a certain localized energy estimate, we prove the existence portion of the Strauss conjecture on asymptotically flat manifolds, possibly exterior to a compact domain, when the spatial dimension is 3 or 4. In particular, this…
We reformulate the standard local equations of general relativity for asymptotically flat spacetimes in terms of two non-local quantities, the holonomy $H$ around certain closed null loops on characteristic surfaces and the light cone cut…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
We use qualitative arguments combined with numerical simulations to argue that, in the approach to the singularity in a vacuum solution of Einstein's equations with $T^2$ isometry, the evolution at a generic point in space is an endless…
In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for…
Quite a number of distinct versions of Bartnik's definition of quasi-local mass appear in the literature, and it is not a priori clear that any of them produce the same value in general. In this paper we make progress on reconciling these…