A new look at the Bondi–Sachs energy–momentum* *Supported by the Marsden Fund Council from Government funding, managed by Royal Society Te Apārangi. JF is grateful to L Szabados for several discussions on this topic.

Abstract

How does one compute the Bondi mass on an arbitrary cut of null infinity when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi–Sachs energy–momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of so that most of the available formulations of the Bondi energy–momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy–momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the ‘co-curvature’, a naturally appearing quantity closely related to the Gauß curvature on a cut of .