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

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.