Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. III. On the determination of radiation

TL;DR

This paper develops an intrinsic, accurate method for extracting gravitational radiation in numerical relativity, operating directly at null infinity without additional approximations, applicable to Maxwell and gravitational fields.

Contribution

It introduces a radiation extraction procedure within conformal methods that accurately mimics physical measurements at null infinity in asymptotically flat spacetimes.

Findings

Defines a detector at infinity using idealized local observers.

Provides a detailed approach for Maxwell fields and extends to gravity.

Ensures radiation extraction is intrinsic and accurate at null infinity.

Abstract

We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which mimics the physical measurement process. It operates entirely intrisically within $\scri^+$ so that there is no further approximation necessary apart from the basic assumption that the arena be an asymptotically flat space-time. We define the notion of a detector at infinity by idealising local observers in Minkowski space. A detailed discussion is presented for Maxwell fields and the generalisation to linearised and full gravity is performed by way of the similar structure of the asymptotic fields.