Big deformations near infinity

Big Deformations near 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...

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...

Initial data for stationary space-times near space-like infinity

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the p...

On Uniqueness of Kerr Space-time near null infinity

We re-express the Kerr metric in standard Bondi-Saches’ coordinate near null infinity I+. Using the uniqueness result of characteristic initial value problem, we prove the Kerr metric is the only asymptotic flat, stationary, axial symmetric, Type-D solution of vacuum Einstein equation. The Taylor series of Kerr space-time is expressed in terms of B-S coordinates and the N-P constants have been ...