Convergent null data expansions at space-like infinity of stationary vacuum solutions

TL;DR

This paper characterizes the asymptotic behavior of stationary vacuum solutions to Einstein's equations near spatial infinity using null data sequences, establishing conditions for their convergent expansions and linking them to Hansen's multipoles.

Contribution

It introduces a complete characterization of asymptotically flat stationary vacuum solutions via null data and growth estimates, connecting formal expansions to physical multipole moments.

Findings

Null data sequences determine formal solution expansions.

Necessary growth conditions ensure convergence of series.

Complete characterization of solutions near spatial infinity.

Abstract

We present a characterization of the asymptotics of all asymptotically flat stationary vacuum solutions of Einstein's field equations. This characterization is given in terms of two sequences of symmetric trace free tensors (we call them the `null data'), which determine a formal expansion of the solution, and which are in a one to one correspondence to Hansen's multipoles. We obtain necessary and sufficient growth estimates on the null data to define an absolutely convergent series in a neighbourhood of spatial infinity. This provides a complete characterization of all asymptotically flat stationary vacuum solutions to the field equations.