Static spacetimes with prescribed multipole moments; a proof of a conjecture by Geroch
arXiv:0906.4247 · doi:10.1088/0264-9381/26/21/215009
Abstract
In this paper we give sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. The proof is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. Since these sufficient conditions agree with already known necessary conditions, this completes the proof of a long standing conjecture due to Geroch.
29 pages