Static vacuum solutions from convergent null data expansions at space-like 
infinity

Friedrich, Helmut

doi:10.1007/s00023-006-0323-3

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Static vacuum solutions from convergent null data expansions at space-like infinity

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Friedrich, Helmut
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Friedrich, H. (2007). Static vacuum solutions from convergent null data expansions at space-like infinity. Annales Henri Poincare, 8(5), 817-884. doi:10.1007/s00023-006-0323-3.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-48AC-B

Abstract

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.