Bondi-type systems near space-like and null infinity

TL;DR

The work integrates Bondi-type asymptotics with a conformal treatment of space-like infinity by representing i^0 as a cylinder I and solving a regular finite initial value problem. Using this framework, it expresses NP-constants in terms of initial data and derives a third-order near-I expansion, while identifying potential logarithmic singularities controlled by asymptotic regularity conditions. The approach also provides a practical bridge between Bondi gauge and the NP-gauge, offering insights for both analytical understanding and numerical computation of entire asymptotically flat space-times. Overall, it demonstrates that key quantities defined at null infinity can be recovered from initial data near space-like infinity and that the framework supports smooth extensions under suitable conditions.

Abstract

We discuss how asymptotic quantities, originally introduced on null infinity in terms of Bondi-type gauge conditions, can be calculated near space-like infinity to any desired precision.