Bondi-type systems near space-like infinity and the calculation of the NP-constants

TL;DR

This paper connects Bondi systems near space-like infinity with gauge conditions based on Einstein propagation, enabling the calculation of NP-constants from initial data for certain space-times.

Contribution

It introduces a method to relate Bondi systems to Einstein propagation gauges and derives expressions for NP-constants from initial data in specific space-times.

Findings

Derived expansions for fields near space-like infinity.

Expressed NP-constants in terms of initial data.

Calculated expansions up to third order.

Abstract

We relate Bondi systems near space-like infinity to another type of gauge conditions. While the former are based on null infinity, the latter are defined in terms of Einstein propagation, the conformal structure, and data on some Cauchy hypersurface. For a certain class of time symmetric space-times we study an expansion which allows us to determine the behavior of various fields arising in Bondi systems in the region of space-time where null infinity touches space-like infinity. The coefficients of these expansions can be read off from the initial data. We obtain in particular expressions for the constants discovered by Newman and Penrose (NP-constants) in terms of the initial data. For this purpose we calculate a certain expansion up to 3rd order.