Linearized gravitational waves near space-like and null infinity

TL;DR

This paper investigates linear gravitational perturbations near spatial and null infinity in Minkowski space using Friedrich's conformal framework, demonstrating accurate extraction of gravitational radiation at null infinity.

Contribution

It applies Friedrich's conformal field equations to linear gravitational waves, showing how to reach null infinity and extract radiation in a numerical setting.

Findings

Null infinity can be reached from initial data on asymptotically Euclidean slices.

The radiation field can be accurately extracted at null infinity.

Spherical symmetry allows decomposition into multipoles for analysis.

Abstract

Linear perturbations on Minkowski space are used to probe numerically the remote region of an asymptotically flat space-time close to spatial infinity. The study is undertaken within the framework of Friedrich's conformal field equations and the corresponding conformal representation of spatial infinity as a cylinder. The system under consideration is the (linear) zero-rest-mass equation for a spin-2 field. The spherical symmetry of the underlying background is used to decompose the field into separate non-interacting multipoles. It is demonstrated that it is possible to reach null-infinity from initial data on an asymptotically Euclidean hyper-surface and that the physically important radiation field can be extracted accurately on $\scri^+$.