Convergent Null Data Expansions at Space-Like Infinity of Stationary Vacuum Solutions

ANDRÉS E. ACEÑA

Annales Henri Poincare

Birkhäuser Basel

Lugar: Basel; Año: 2009 vol. 10 p. 275 - 337

1424-0637

We present a characterization of the asymptotics of all asymptotically flat, stationary solutions with non-vanishing ADM mass to Einstein’s vacuum 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 neighborhood of spatial infinity. This provides a complete characterization of all asymptotically flat, stationary vacuum solutions to the field equations with non-vanishing ADM mass.