相关论文: The conformal Einstein field equations and the loc…

We adapt Luk's analysis of the characteristic initial value problem in General Relativity to the asymptotic characteristic problem for the conformal Einstein field equations to demonstrate the local existence of solutions in a neighbourhood…

We obtain necessary and sufficient conditions for an initial data set for the vacuum conformal Einstein field equations to give rise to a spacetime development in possession of a Killing spinor. The fact that the conformal Einstein field…

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…

This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…

The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…

We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…

One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…

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…

We prove a semi-global gauge-invariant estimate for the solutions of the characteristic initial value problem associated with the coupled Einstein-Yang-Mills equations. In particular, we prove the existence of \textit{a} future development…

A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…

We derive, in 3+1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich's conformal field equations. We analyse their equivalence to Einstein's vacuum field equations when appropriate constraint…

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…

We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable…

The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…

In a recent work, Ringstr\"om proposed a geometric notion of initial data on big bang singularities. Moreover, he conjectured that initial data on the singularity could be used to parameterize quiescent solutions to Einstein's equations;…

In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…

We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future complete null cone with suitable decay, and show that the solution exists uniformly around the null cone for general such…

We prove the stability of de Sitter space-time as a solution to the Einstein-Vlasov system with massless particles. The semi-global stability of Minkowski space-time is also addressed. The proof relies on conformal techniques, namely…

This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…