Static spacetimes with prescribed multipole moments; a proof of a conjecture by Geroch

Details Static spacetimes with prescribed multipole moments; a proof of a conjecture by Geroch Static spacetimes with prescribed multipole moments; a proof of a conjecture by Geroch

2009-06-23

arxiv.org/abs/0906.4247v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages

Scientific paper

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.

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