Asymptotic flatness and algebraically special metrics

Abstract

We develop a formalism that allows us to obtain an approximate Bondi–Sachs form of metrics which are asymptotically flat at null infinity . We find conditions which assure that algebraically special metrics fall into this class. For these metrics we calculate the Bondi mass aspect, the angular momentum aspect and the news function.

No news for Kerr-Schild fields

“…In Section II the notation for twisting algebraically special metrics is fixed and the expressions for the Bondi mass and the news function are given according to [21]. In Section III the condition for no news is discussed and different classes of metrics that satisfy it are given.…”

Kerr–Schild metrics and gravitational radiation

“…In [15] we have formulated conditions assuring that the twisting algebraically special metric satisfying (2) is asymptotically flat at I + . These metrics are expressed in terms of the coordinates (u, r, ξ,ξ):…”

“…We use the same definition of asymptotic flatness at I + as in [8] and [15]. The notation aims to be as close as possible to that of [15].…”

“…The notation aims to be as close as possible to that of [15]. The Penrose conformal factor is denoted by , an equality on I + is denoted by= .…”

“…This formula corresponds to standard spinor definitions of angular momentum at I + (see [18] and references therein.) The procedure of findingM and κ A is described in detail in [8] and [15].…”