Einstein's equations near spatial infinity

Numerical calculations near spatial infinity

After describing in short some problems and methods regarding the smoothness of null infinity for isolated systems, I present numerical calculations in which both spatial and null infinity can be studied. The reduced conformal field equations based on the conformal Gauss gauge allow us in spherical symmetry to calculate numerically the entire Schwarzschild-Kruskal spacetime in a smooth way incl...

Does asymptotic simplicity allow for radiation near spatial infinity?

A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that generic time symmetric initial data with an analytic conformal metric at spatial infinity will give rise to developments with a certain type of logarithmic s...

Big Deformations near Infinity

The Positive Mass Theorem near Null Infinity

The definition of the total energy-momentum at spatial infinity was given by Arnowitt-Desser-Misnerfor in asymptotically flat spacetimes [1]. The positivity of the ADM mass was proved by Schoen and Yau in a nontrivial isolated physical system which satisfies the dominant energy condition [16, 17, 18]. Later it was proved by Witten using spinors [22]. The positive mass theorem plays a fundamenta...

The Maxwell field on the Schwarzschild spacetime: behaviour near spatial infinity

The behaviour of the Maxwell field near one of the spatial infinities of the Schwarzschild solution is analysed by means of the transport equations implied by the Maxwell equations on the cylinder at spatial infinity. Initial data for the Maxwell equations will be assumed to be expandable in terms of powers of a coordinate ρ measuring the geodesic distance to spatial infinity (in the conformal ...