Static vacuum solutions from convergent null data expansions at space-like infinity. (English) Zbl 1203.83011
Summary: We study formal expansions of asymptotically flat solutions to the static vacuum field equations which are determined by minimal sets of freely specifyable data referred to as ‘null data’. These are given by sequences of symmetric trace free tensors at space-like infinity of increasing order. They are \(1 : 1\) related to the sequences of Geroch multipoles. Necessary and sufficient growth estimates on the null data are obtained for the formal expansions to be absolutely convergent. This provides a complete characterization of all asymptotically flat solutions to the static vacuum field equations.
MSC:
83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
83C15 | Exact solutions to problems in general relativity and gravitational theory |
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
83E05 | Geometrodynamics and the holographic principle |
35L15 | Initial value problems for second-order hyperbolic equations |