Related papers: Does asymptotic simplicity allow for radiation nea…
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…
Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this ends a…
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…
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…
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…
This paper initiates a series of works dedicated to the rigorous study of the precise structure of gravitational radiation near infinity. We begin with a brief review of an argument due to Christodoulou [1] stating that Penrose's proposal…
Certain aspects of the behaviour of the gravitational field near null and spatial infinity for the developments of asymptotically Euclidean, conformally flat initial data sets are analysed. Ideas and results from two different approaches…
We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubisic and…
Penrose's idea of asymptotic flatness provides a framework for understanding the asymptotic structure of gravitational fields of isolated systems at null infinity. However, the studies of the asymptotic behaviour of fields near spatial…
A study of the linearised gravitational field (spin 2 zero-rest-mass field) on a Minkowski background close to spatial infinity is done. To this purpose, a certain representation of spatial infinity in which it is depicted as a cylinder is…
We describe asymptotic symmetries at spatial infinity of asymptotically flat spacetimes within the context of a generalization of the Beig-Schmidt-Ashtekar-Romano-framework. We demonstrate that it is possible to relax certain smoothness…
A new approach to space-time asymptotics is presented, refining Penrose's idea of conformal transformations with infinity represented by the conformal boundary of space-time. Generalizing examples such as flat and Schwarzschild space-times,…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is…
We describe our present understanding of the relations between the behaviour of asymptotically flat Cauchy data for Einstein's vacuum field equations near space-like infinity and the asymptotic behaviour of their evolution in time at null…
Linear zero-rest-mass fields generically develop logarithmic singularities at the critical sets where spatial infinity meets null infinity. Friedrich's representation of spatial infinity is ideally suited to study this phenomenon. These…
The asymptotic structure of space-time is studied by imposing conditions on the asymptotics of the metric. These conditions are weak enough to include large classes of physically relevant isolated space-times, but have a rich enough…
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…
We investigate the asymptotic symmetries of asymptotically flat spacetimes at spatial infinity. We propose a new symplectic structure and conservative boundary conditions in a polyhomogeneous Beig-Schmidt expansion. The asymptotic…
In case of a spherically symmetric non-linear scalar field (SF) in flat space, besides singularity at the center, spherical singularities can occur for non-zero values of radial variable $r>0$. We show that in the General Relativity the…