The Einstein metrics with smooth scri

TL;DR

This paper studies Einstein solutions with a non-zero cosmological constant that admit smooth conformal infinity, analyzing their metric structure and constraints in Bondi-Sachs coordinates.

Contribution

It provides a detailed recursive framework for Einstein metrics with smooth scri when mbdaneq 0, highlighting the placement of free data and constraints.

Findings

Metrics expanded in inverse powers of affine distance r

All free data are located on scri for mbdaneq 0

Linear differential constraints on Bondi mass and angular momentum aspects

Abstract

We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification with smooth scri $\mathscr{I^+}$. Metrics are written in the Bondi-Sachs coordinates and expanded into inverse powers of the affine distance $r$. Unlike in the case $\Lambda=0$ all free data are located on the scri. There are linear differential constraints on the Bondi mass and angular momentum aspects. All other components of metrics are defined in a recursive way.